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Research

In page navigation: Applied Mathematics 1
  • Staff Members A-Z
  • Teaching
  • Workshop on Recent Developments in Modelling, Analysis, and Simulation of Processes in Porous Media
  • Research
  • Former Members
    • Dr. Vadym Aizinger
    • Dr. Apratim Bhattacharya
    • Astrid Bigott
    • Dr. Leon Bungert
    • Prof. Dr. Martin Burger
    • Dr. Tobias Elbinger
    • PD Dr. Florian Frank
    • Dr. Antonio Esposito
    • Dr. Lea Föcke
    • Dr. Hubertus Grillmeier
    • Samira Kabri
    • Dr. Alicja Kerschbaum
    • Prof. Dr. Peter Knabner
      • Curriculum Vitae
      • Research
      • Teaching
    • Dr. habil. Nicolae Suciu
    • Dr. Jonas Knoch
    • Dr. Markus Knodel
    • Alice Lieu, PhD
    • Dr. Balthasar Reuter
    • Dr. Andreas Rupp
    • Doris Schneider
    • Dr. habil. Raphael Schulz
    • Dr. Oliver Sieber
    • Dr. Philipp Wacker
    • Lukas Weigand
    • Dr. Patrick Weiß
    • Dr. Philipp Werner
    • Dr. Simon Zech
  • Upcoming events

Research

Referenzen

 

Google Scholar

An exact overview can be found here.

 

Google Scholar.

 

 

Web of Science

An exact overview can be found here.

 

Web of Science.

Scopus

An exact overview can be found here.

 

 

Scopus.

Books

Information about published books can be found here.

Publications

  • Angermann L., Knabner P., Rupp A.:
    Error estimates for completely discrete FEM in energy-type and weaker norms
    In: Numerical Methods For Partial Differential Equations (2024)
    ISSN: 0749-159X
    DOI: 10.1002/num.23106
    BibTeX: Download
  • Gärttner S., Knabner P., Ray N.:
    Local existence of strong solutions to micro-macro models for reactive transport in evolving porous media
    In: European Journal of Applied Mathematics 35 (2024), p. 127-154
    ISSN: 0956-7925
    DOI: 10.1017/S095679252300013X
    BibTeX: Download

  • Musch M., Rupp A., Aizinger V., Knabner P.:
    Hybridizable discontinuous Galerkin method with mixed-order spaces for non-linear diffusion equations with internal jumps
    In: GEM - International Journal on Geomathematics 14 (2023), Article No.: 18
    ISSN: 1869-2672
    DOI: 10.1007/s13137-023-00228-7
    BibTeX: Download

  • Elbinger T., Knabner P.:
    Efficient numerical solution of micro-macro models for multicomponent transport and reaction problems in porous media
    In: Applicable Analysis (2022)
    ISSN: 0003-6811
    DOI: 10.1080/00036811.2022.2097906
    BibTeX: Download
  • Gärttner S., Frolkovič P., Knabner P., Ray N.:
    Efficiency of micro-macro models for reactive two-mineral systems
    In: Multiscale Modeling & Simulation 20 (2022), p. 433-461
    ISSN: 1540-3459
    DOI: 10.1137/20M1380648
    BibTeX: Download
  • Kelm M., Gärttner S., Bringedal C., Flemisch B., Knabner P., Ray N.:
    Comparison study of phase-field and level-set method for three-phase systems including two minerals
    In: Computational Geosciences 26 (2022), p. 545 - 570
    ISSN: 1420-0597
    DOI: 10.1007/s10596-022-10142-w
    BibTeX: Download
  • Knodel MM., Kräutle S., Knabner P.:
    Global implicit solver for multiphase multicomponent flow in porous media with multiple gas components and general reactions: Global implicit solver for multiple gas components
    In: Computational Geosciences 26 (2022), p. 697-724
    ISSN: 1420-0597
    DOI: 10.1007/s10596-022-10140-y
    URL: https://link.springer.com/article/10.1007/s10596-022-10140-y
    BibTeX: Download

  • Kräutle S., Hodai J., Knabner P.:
    Robust simulation of mineral precipitation-dissolution problems with variable mineral surface area
    In: Journal of Engineering Mathematics 129 (2021)
    ISSN: 0022-0833
    DOI: 10.1007/s10665-021-10132-4
    URL: https://link.springer.com/article/10.1007/s10665-021-10132-4
    BibTeX: Download
  • Metzger S., Knabner P.:
    Homogenization of Two-Phase Flow in Porous Media From Pore to Darcy Scale: A Phase-Field Approach
    In: Multiscale Modeling & Simulation 19 (2021), p. 320-343
    ISSN: 1540-3459
    DOI: 10.1137/19M1287705
    BibTeX: Download

  • Alecsa CD., Boros I., Frank F., Knabner P., Nechita M., Prechtel A., Rupp A., Suciu N.:
    Numerical benchmark study for flow in highly heterogeneous aquifers
    In: Advances in Water Resources (2020), p. 103558
    ISSN: 0309-1708
    DOI: 10.1016/j.advwatres.2020.103558
    BibTeX: Download
  • Gärttner S., Frolkovič P., Knabner P., Ray N.:
    Efficiency and Accuracy of Micro-Macro Models for Mineral Dissolution
    In: Water Resources Research 56 (2020), Article No.: e2020WR027585
    ISSN: 0043-1397
    DOI: 10.1029/2020WR027585
    BibTeX: Download
  • Knodel M., Kräutle S., Knabner P.:
    Global implicit solver for multiphase multicomponent flow in porous media with multiple gas phases and general reactions
    In: Robert Klöfkorn, Eirik Keilegavlen, Florin A. Radu, Jürgen Fuhrmann (ed.): Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, Heidelberg: Springer, 2020, p. 595-603 (Finite Volumes for Complex Applications, Vol.9)
    ISBN: 978-3-030-43650-6

    DOI: 10.1007/978-3-030-43651-3_56
    URL: https://www1.am.uni-erlangen.de/research/preprint/pr406.pdf
    BibTeX: Download
  • Reuter B., Hajduk H., Rupp A., Frank F., Aizinger V., Knabner P.:
    FESTUNG 1.0: Overview, usage, and example applications of the MATLAB/GNU Octave toolbox for discontinuous Galerkin methods
    In: Computers & Mathematics with Applications (2020)
    ISSN: 0898-1221
    DOI: 10.1016/j.camwa.2020.08.018
    BibTeX: Download
  • Reuter B., Rupp A., Aizinger V., Frank F., Knabner P.:
    FESTUNG: A MATLAB / GNU Octave Toolbox for the Discontinuous Galerkin Method. Part IV: Generic Problem Framework and Model-Coupling Interface
    In: Communications in Computational Physics 28 (2020), p. 827-876
    ISSN: 1815-2406
    DOI: 10.4208/cicp.OA-2019-0132
    BibTeX: Download

  • Brunner F., Knabner P.:
    A global implicit solver for miscible reactive multiphase multicomponent flow in porous media
    In: Computational Geosciences 23 (2019), p. 127-148
    ISSN: 1420-0597
    DOI: 10.1007/s10596-018-9788-7
    BibTeX: Download
  • Class H., Knabner P., Pop IS., Radu FA.:
    Multiphase, multicomponent flow in deformable porous media: modelling and simulation (Dedicated to Prof. Dr.-Ing. Rainer Helmig on the occasion of his 60th birthday)
    In: Computational Geosciences 23 (2019), p. 203-205
    ISSN: 1420-0597
    DOI: 10.1007/s10596-019-9814-4
    BibTeX: Download
  • Knabner P., Reuter B., Schulz R.:
    Mit Mathe richtig anfangen Eine Einführung mit integrierter Anwendung der Programmiersprache Python
    Berlin Heidelberg: Springer Spektrum, 2019
    ISBN: 978-3-662-59229-8
    DOI: 10.1007/978-3-662-59230-4
    BibTeX: Download
  • Molins S., Knabner P.:
    Multiscale Approaches in Reactive Transport Modeling
    In: Reviews in Mineralogy & Geochemistry 85 (2019), p. 27-48
    ISSN: 1529-6466
    DOI: 10.2138/rmg.2019.85.2
    BibTeX: Download
  • Reuter B., Rupp A., Aizinger V., Knabner P.:
    Discontinuous Galerkin method for coupling hydrostatic free surface flows to saturated subsurface systems
    In: Computers & Mathematics with Applications 77 (2019), p. 2291-2309
    ISSN: 0898-1221
    DOI: 10.1016/j.camwa.2018.12.020
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2018/2018_ReuterRuppAizingerKn_DiscontGalerkinMethForCouplHydrostFreeSurfaceFlowsToSaturSubsurfSyst
    BibTeX: Download
  • Schulz R., Ray N., Zech S., Rupp A., Knabner P.:
    Beyond Kozeny-Carman: Predicting the Permeability in Porous Media
    In: Transport in Porous Media (2019)
    ISSN: 0169-3913
    DOI: 10.1007/s11242-019-01321-y
    BibTeX: Download
  • Wacker PK., Knabner P.:
    Wavelet-Based Priors Accelerate Maximum-a-Posteriori Optimization in Bayesian Inverse Problems
    In: Methodology and Computing in Applied Probability 22 (2019), p. 853-879
    ISSN: 1387-5841
    DOI: 10.1007/s11009-019-09736-2
    BibTeX: Download

  • Aizinger V., Rupp A., Schütz J., Knabner P.:
    Analysis of a mixed discontinuous Galerkin method for instationary Darcy flow
    In: Computational Geosciences 22 (2018), p. 179-194
    ISSN: 1420-0597
    DOI: 10.1007/s10596-017-9682-8
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2018/2018_AizingerRuppSchuetzKn_AnalysisOfAMixedDiscontinuousGalerkinForDarcyFlow
    BibTeX: Download
  • Gahn M., Neuss-Radu M., Knabner P.:
    EFFECTIVE INTERFACE CONDITIONS FOR PROCESSES THROUGH THIN HETEROGENEOUS LAYERS WITH NONLINEAR TRANSMISSION AT THE MICROSCOPIC BULK-LAYER INTERFACE
    In: Networks and Heterogeneous Media 13 (2018), p. 609-640
    ISSN: 1556-1801
    DOI: 10.3934/nhm.2018028
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2018/2018_GahnNeussraduKn_EffectInterfCondForProcThrouThinHeterogenLayerWthNonlinearTransmissAtTeMicroscBulklayerInterface
    BibTeX: Download
  • Jaust A., Reuter B., Aizinger V., Schütz J., Knabner P.:
    FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation
    In: Computers & Mathematics with Applications 75 (2018), p. 4505-4533
    ISSN: 0898-1221
    DOI: 10.1016/j.camwa.2018.03.045
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2018/2018_JaustReuterAizingerSchuetzKn_FestungAMatlabGnuPartIIIHDG
    BibTeX: Download
  • Knabner P., Barth W.:
    Lineare Algebra. Grundlagen und Anwendungen, 2. Auflage
    Springer, 2018
    ISBN: 978-3-662-55599-6
    BibTeX: Download
  • Ray N., Rupp A., Schulz R., Knabner P.:
    Old and New Approaches Predicting the Diffusion in Porous Media
    In: Transport in Porous Media 124 (2018), p. 803-824
    ISSN: 0169-3913
    DOI: 10.1007/s11242-018-1099-x
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2018/2018_RayRuppSchulzKn_OldAndNewApproachesPredictingTheDiffInPM
    BibTeX: Download
  • Rupp A., Knabner P., Dawson C.:
    A local discontinuous Galerkin scheme for Darcy flow with internal jumps
    In: Computational Geosciences 22 (2018), p. 1149-1159
    ISSN: 1420-0597
    DOI: 10.1007/s10596-018-9743-7
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2018/2018_RuppKnDawson_ALocalDiscontinuousGalerkinSchemeForDarcy
    BibTeX: Download

  • Eck C., Garcke H., Knabner P.:
    Mathematical Modeling
    Springer International Publishing, 2017
    (Springer Undergraduate Mathematics Series)
    ISBN: 978-3-319-55160-9
    DOI: 10.1007/978-3-319-55161-6
    BibTeX: Download
  • Frank F., Knabner P.:
    Convergence analysis of a BDF2/mixed finite element discretization of a Darcy–Nernst–Planck–Poisson system
    In: Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique 51 (2017), p. 1883-1902
    ISSN: 0764-583X
    DOI: 10.1051/m2an/2017002
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_FrankKn_ConvergenceAnalysisOfBDFDarcyNernstPlanckPoissonSystem
    BibTeX: Download
  • Gahn M., Neuss-Radu M., Knabner P.:
    Derivation of an Effective Model for Metabolic Processes in Living Cells Including Substrate Channeling
    In: Vietnam Journal of Mathematics 45 (2017), p. 265-293
    ISSN: 0866-7179
    DOI: 10.1007/s10013-016-0227-6
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_GahnNeussraduKn_DerivationOfAnEffectiveModelForMetaProcSubstrateChanneling
    BibTeX: Download
  • Gahn M., Neuss-Radu M., Knabner P.:
    DERIVATION OF EFFECTIVE TRANSMISSION CONDITIONS FOR DOMAINS SEPARATED BY A MEMBRANE FOR DIFFERENT SCALING OF MEMBRANE DIFFUSIVITY
    In: Discrete and Continuous Dynamical Systems 10 (2017), p. 773-797
    ISSN: 1078-0947
    DOI: 10.3934/dcdss.2017039
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_GahnNeussraduKn_DerivOfEffectTransmissConditForDomainSeparByMembraneForDiffScalOfMembrDiffusivity
    BibTeX: Download
  • Hoffmann J., Kräutle S., Knabner P.:
    Existence and uniqueness of a global solution for reactive transport with mineral precipitation-dissolution and aquatic reactions in porous media
    In: SIAM Journal on Mathematical Analysis 49 (2017), p. 4812-4837
    ISSN: 0036-1410
    DOI: 10.1137/16M1109266
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_HoffmannKraeutleKn_ExistenceAndUniquenessOfGlobalSolutionForReactiveTransWithMineralPreDissAndAquaReactInPM
    BibTeX: Download
  • Knabner P., Rannacher R.:
    A Priori Error Analysis for the Galerkin Finite Element Semi-discretization of a Parabolic System with Non-Lipschitzian Nonlinearity
    In: Vietnam Journal of Mathematics (2017), p. 179-198
    ISSN: 0866-7179
    DOI: 10.1007/s10013-016-0214-y
    URL: https://link.springer.com/content/pdf/10.1007/s10013-016-0214-y.pdf
    BibTeX: Download
  • Mahato HS., Kräutle S., Böhm M., Knabner P.:
    Upscaling of a system of semilinear parabolic partial differential equations coupled with a system of nonlinear ordinary differential equations originating in the context of crystal dissolution and precipitation inside a porous medium: existence theory and periodic homogenization
    In: Advances in Mathematical Sciences and Applications 26 (2017), p. 39-81
    ISSN: 1343-4373
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_MahatoKraeutleKnBoehm_UpscalingOfASystemOfDiffusionReactionEquations
    BibTeX: Download
  • Merz W., Knabner P.:
    Endlich gelöst! Aufgaben zur Mathematik für Ingenieure und Naturwissenschaftler Band 2: Analysis in R^n und gewöhnliche Differentialgleichungen
    Springer Spektrum, 2017
    ISBN: 978-3-662-54782-3
    DOI: 10.1007/978-3-662-54783-0
    BibTeX: Download
  • Merz W., Knabner P.:
    Mathematik für Inenieure und Naturwissenschaftler: Band 2 Analysis in R^n und gewöhnliche Differentialgleichungen
    Springer Spektrum, 2017
    ISBN: 978-3-662-54780-9
    DOI: 10.1007/978-3-662-54781-6
    BibTeX: Download
  • Rupp A., Knabner P.:
    Convergence order estimates of the local discontinuous Galerkin method for instationary Darcy flow
    In: Numerical Methods For Partial Differential Equations 33 (2017), p. 1374-1394
    ISSN: 0749-159X
    DOI: 10.1002/num.22150
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_RuppKn_ConvergenceOrderEstimatesOfTheLocalDisGMForInstDarcyFlow
    BibTeX: Download
  • Schulz R., Knabner P.:
    An effective model for biofilm growth made by chemotactical bacteria in evolving porous media
    In: SIAM Journal on Applied Mathematics 77 (2017), p. 1653-1677
    ISSN: 0036-1399
    DOI: 10.1137/16M108817X
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_SchulzKn_AnEffectiveModelForBiofilmGrowthInEvolvinPM
    BibTeX: Download
  • Schulz R., Knabner P.:
    Derivation and analysis of an effective model for biofilm growth in evolving porous media
    In: Mathematical Methods in the Applied Sciences 40 (2017), p. 2930-2948
    ISSN: 0170-4214
    DOI: 10.1002/mma.4211
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_SchulzKn_DerivAnalysOfEffectModelForBiofilmGrowthInEvolvPM
    BibTeX: Download

  • Brunner F., Fischer J., Knabner P.:
    Analysis of a Modified Second-Order Mixed Hybrid $BDM_1$ Finite Element Method for Transport Problems in Divergence Form
    In: SIAM Journal on Numerical Analysis 54 (2016), p. 2359-2378
    ISSN: 0036-1429
    DOI: 10.1137/15M1035379
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_BrunnerFischerKn_AnalysisOfModifSecondOrderMixBDMInDivergenceForm
    BibTeX: Download
  • Elbinger T., Gahn M., Hante F., Voll L., Leugering G., Knabner P., Neuss-Radu M.:
    Model-Based Design of Biochemical Microreactors
    In: Frontiers in Bioengineering and Biotechnology (2016)
    ISSN: 2296-4185
    DOI: 10.3389/fbioe.2016.00013
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_ElbingerGahnNeusRaduHanteVollLeugering_ModelBasedDesignOfBioMicroReact
    BibTeX: Download
  • Gahn M., Neuss-Radu M., Knabner P.:
    HOMOGENIZATION OF REACTION-DIFFUSION PROCESSES IN A TWO-COMPONENT POROUS MEDIUM WITH NONLINEAR FLUX CONDITIONS AT THE INTERFACE
    In: SIAM Journal on Applied Mathematics 76 (2016), p. 1819-1843
    ISSN: 0036-1399
    DOI: 10.1137/15M1018484
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_GahnNeussraduKn_HomoOfReactionDiffusionWirhNonlinearFluxCondition
    BibTeX: Download
  • Reuter B., Aizinger V., Wieland M., Frank F., Knabner P.:
    FESTUNG: A MATLAB /GNU Octave toolbox for the discontinuous Galerkin method. Part II: Advection operator and slope limiting
    In: Computers & Mathematics with Applications 72 (2016), p. 1896-1925
    ISSN: 0898-1221
    DOI: 10.1016/j.camwa.2016.08.006
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_ReuterAizingerWielandFrankKn_FestungAMatLabGnuPartII
    BibTeX: Download
  • Schulz R., Ray N., Frank F., Mahato H., Knabner P.:
    Strong solvability up to clogging of an effective diffusion-precipitation model in an evolving porous medium
    In: European Journal of Applied Mathematics (2016), p. 1-29
    ISSN: 0956-7925
    DOI: 10.1017/S0956792516000164
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_SchulzRayFrankMahatoKn_StrongSolvUpToCloggingInAnEvolvingPM
    BibTeX: Download
  • Schüler L., Suciu N., Knabner P., Attinger S.:
    A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers
    In: Advances in Water Resources 96 (2016), p. 55-67
    ISSN: 0309-1708
    DOI: 10.1016/j.advwatres.2016.06.012
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_SchuelerSuciuKnAttinger_ATimeDependMixModelToClosePDFequatForTranspInHeterogAquifers
    BibTeX: Download
  • Suciu N., Schüler L., Attinger S., Knabner P.:
    Towards a filtered density function approach for reactive transport in groundwater
    In: Advances in Water Resources 90 (2016), p. 83-98
    ISSN: 0309-1708
    DOI: 10.1016/j.advwatres.2016.02.016
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_SuciuSchuelerAttingerKn_TowardsFilterDensityFunctApproaForReactTranspInGroundwater
    BibTeX: Download

  • Elbinger T., Gahn M., Neuss-Radu M., Knabner P.:
    Simulation of Processes in Living Cells: Towards the Modelling of Metabolic Channeling
    In: A. Ibrahimbegovic, J.-M. Ghidaglia, A. Serdarevic, E. Ilic- Georgijevic, M. Hrasnica, S. Dolarevic, N. Ademovic (ed.): 2nd International Conference on Multi-scale Computational Methods for Solids and Fluids, 2015, p. 44-47
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2015/2015_Proc_ElbingerGahnNeussraduKn_SimulOfProcessInLivCellsTowardsModellingOfMetaboliChannel
    BibTeX: Download
  • Frank F., Reuter B., Aizinger V., Knabner P.:
    FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part I: Diffusion operator
    In: Computers & Mathematics with Applications 70 (2015), p. 11 - 46
    ISSN: 0898-1221
    DOI: 10.1016/j.camwa.2015.04.013
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2015/2015_FrankReuterAizingerKn_FestungAMatlabGnuPartIDiffusionOperator
    BibTeX: Download
  • Krehel O., Muntean A., Knabner P.:
    Multiscale modeling of colloidal dynamics in porous media including aggregation and deposition
    In: Advances in Water Resources 86 (2015), p. 209-216
    ISSN: 0309-1708
    DOI: 10.1016/j.advwatres.2015.10.005
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2015/2015_KrehelMunteanKn_MultiscModelOfColloidDynamInPMinclAggregDepos
    BibTeX: Download
  • Ray N., Elbinger T., Knabner P.:
    Upscaling the flow and transport in an evolving porous medium with general interaction potentials
    In: SIAM Journal on Applied Mathematics 75 (2015), p. 2170-2192
    ISSN: 0036-1399
    DOI: 10.1137/140990292
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2015/2015_RayElbingerKn_UpscalingFlowTransInAnEvolvingPMWithGeneralInterPotentials
    BibTeX: Download
  • Suciu N., Attinger S., Radu AF., Vamo̧s C., Vanderborght J., Vereecken H., Knabner P.:
    Solute transport in aquifers with evolving scale heterogeneity
    In: Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica 23 (2015), p. 167-186
    ISSN: 1844-0835
    DOI: 10.1515/auom-2015-0054
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2015/2015_SuciuAttingerRaduVamocsVanderborghtVereeckenKn_SoluteTransportinAquifersWithEvolvingScaleHetereo
    BibTeX: Download
  • Suciu N., Radu AF., Attinger S., Schüler L., Knabner P.:
    A Fokker-Planck approach for probability distributions of species concentrations transported in heterogeneous media
    In: Journal of Computational and Applied Mathematics 289 (2015), p. 241-252
    ISSN: 0377-0427
    DOI: 10.1016/j.cam.2015.01.030
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2015/2015_SuciuRaduAttingerSchuelerKn_AFokkerPlanckApproachForProbabDistrOfSpecConcTransInHetrogeneousMedia
    BibTeX: Download
  • Suciu N., Schüler L., Radu AF., Attinger S., Vamo̧s C., Knabner P.:
    Consistency issues in pdf methods
    In: Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica 23 (2015), p. 187-208
    ISSN: 1844-0835
    DOI: 10.1515/auom-2015-0055
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2015/2015_SuciuSchuelerRaduAttingerVamosKn_ConsistencyIssuesInPDFMethods
    BibTeX: Download

  • Brunner F., Frank F., Knabner P.:
    FV upwind stabilization of FE discretizations for advection-diffusion problems
    7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7 (Berlin, 15-06-2014 - 20-06-2014)
    In: Fuhrmann Jürgen, Ohlberger Mario, Rohde Christian (ed.): Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects 2014
    DOI: 10.1007/978-3-319-05684-5_16
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2014/2014_BrunnerFrankKn_FVUpwindStabOfFEForAdvancedDiffProblems
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  • Brunner F., Radu AF., Knabner P.:
    Analysis of an upwind-mixed hybrid finite element method for transport problems
    In: SIAM Journal on Numerical Analysis 52 (2014), p. 83-102
    ISSN: 0036-1429
    DOI: 10.1137/130908191
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2014/2014_BrunnerRaduKn_AnalysisOfAnUpwindMixedHyTransProblems
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  • Knabner P., Roberts JE.:
    Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture
    In: ESAIM: Mathematical Modelling and Numerical Analysis 48 (2014), p. 1451-1472
    ISSN: 1290-3841
    DOI: 10.1051/m2an/2014003
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2014/2014_KnRoberts_MathemAnalysisOfDiscrFractModelCouplDarcyFlowInMatrixWthDarcyForchheimer
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  • Marchand E., Knabner P.:
    Results of the MoMaS benchmark for gas phase appearance and disappearance using generalized MHFE
    In: Advances in Water Resources 73 (2014), p. 74-96
    ISSN: 0309-1708
    DOI: 10.1016/j.advwatres.2014.07.005
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2014/2014_MarchandKn_ResulOfMoMaBenchmForGasPhasAppearAndDisappearUsingGeneralMHFE
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  • Merz W., Knabner P.:
    Endlich gelöst! Aufgaben zur Mathematik für Ingenieure und Naturwissenschaftler
    Berlin-Heidelberg: Springer, 2014
    (Springer-Lehrbuch)
    ISBN: 978-3-642-54528-3
    DOI: 10.1007/978-3-642-54529-0
    URL: http://www.springer.com/us/book/9783642545283
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  • Knabner P., Barth W.:
    Lineare Algebra: Grundlagen und Anwendungen
    Berlin-Heidelberg: Springer, 2013
    (Springer-Lehrbuch)
    ISBN: 978-3-642-32185-6
    DOI: 10.1007/978-3-642-32186-3
    URL: http://www.springer.com/de/book/9783642321856#aboutBook
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  • Knabner P., Mikelic A., Pop IS.:
    Special issue "Mathematics of Porous Media," dedicated to Professor C.J. van Duijn on the occasion of his 60th anniversary
    In: Computational Geosciences 17 (2013), p. 443-445
    ISSN: 1420-0597
    DOI: 10.1007/s10596-013-9348-0
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2013/2013_KnMikelicPop_SpecialIssueProfDuijn60thAnniversary
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  • Marchand E., Müller T., Knabner P.:
    Fully coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part I: Formulation and properties of the mathematical model
    In: Computational Geosciences 17 (2013), p. 431-442
    ISSN: 1420-0597
    DOI: 10.1007/s10596-013-9341-7
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2013/2013_MarchandMuellerKn_FullyCoupledGeneralizedHybridMixedFinEleApproxPartI
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  • Merz W., Knabner P.:
    Mathematik für Ingenieure und Naturwissenschaftler
    Berlin-Heidelberg: Springer, 2013
    (Springer-Lehrbuch)
    ISBN: 978-3-642-29979-7
    DOI: 10.1007/978-3-642-29980-3
    URL: http://www.springer.com/de/book/9783642299797
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  • Ray N., van Noorden T., Radu AF., Friess W., Knabner P.:
    Drug release from collagen matrices including an evolving microstructure
    In: ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 93 (2013), p. 811-822
    ISSN: 0044-2267
    DOI: 10.1002/zamm.201200196
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2013/2013_RayNoordenRaduFriessKn_DrugReleaseFromCollMatIncludAnEvolvingMicrostruct
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  • Suciu N., Radu AF., Prechtel A., Brunner F., Knabner P.:
    A coupled finite element-global random walk approach to advection-dominated transport in porous media with random hydraulic conductivity
    In: Journal of Computational and Applied Mathematics 246 (2013), p. 27-37
    ISSN: 0377-0427
    DOI: 10.1016/j.cam.2012.06.027
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2013/2013_SuciuRaduPrechtelBrunnerKn_ACoupledFiniteElementGlobalRandomWalkApproach
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  • Bause M., Brunner F., Knabner P., Radu AF.:
    An Improved Optimal Order Mixed Finite Element Method for Semilinear Transport Problems
    In: Andrea Cangiani, Ruslan L. Davidchack, Emmanuil Georgoulis, Alexander N. Gorban, Jeremy Levesley, Michael V. Tretyakov (ed.): Numerical Mathematics and Advanced Applications 2011, Berlin Heidelberg: Springer, 2012, p. 247-255
    ISBN: 978-3-642-33133-6

    DOI: 10.1007/978-3-642-33134-3_27
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2012/2012_BauseBrunnerKnRadu_AnImprOptimOrdMixFinitElemMethodForSemilinTranspProbl
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  • Brunner F., Radu AF., Bause M., Knabner P.:
    Optimal order convergence of a modified BDM 1 mixed finite element scheme for reactive transport in porous media
    In: Advances in Water Resources 35 (2012), p. 163-171
    ISSN: 0309-1708
    DOI: 10.1016/j.advwatres.2011.10.001
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2012/2012_BrunnerRaduBauseKn_OptimalOrderConvergenceOfModifiedBDMMixedFiniteInPM
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  • Herz M., Ray N., Knabner P.:
    Existence and uniqueness of a global weak solution of a Darcy-Nernst-Planck-Poisson system
    In: GAMM-Mitteilungen 35 (2012), p. 191-208
    ISSN: 0936-7195
    DOI: 10.1002/gamm.201210013
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2012/2012_HerzRayKn_ExistAndUniqueOfGlobWeakSolutionDarcyNernPlanPoissSystem
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  • Hoffmann J., Kräutle S., Knabner P.:
    A general reduction scheme for reactive transport in porous media
    In: Computational Geosciences 16 (2012), p. 1081-1099
    ISSN: 1420-0597
    DOI: 10.1007/s10596-012-9304-4
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2012/2012_HoffmannKraeutleKn_AGeneralReductionSchemeForReactTranspInPM
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  • Marchand E., Müller T., Knabner P.:
    Fully coupled generalised hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part II: Numerical scheme and numerical results
    In: Computational Geosciences 16 (2012), p. 691-708
    ISSN: 1420-0597
    DOI: 10.1007/s10596-012-9279-1
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2012/2012_MarchandMuellerKn_FullyCoupledGeneralisedHybridMixedFinEleApproxOf2ph2compFlowInPMPartII
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  • Ray N., Muntean A., Knabner P.:
    Rigorous homogenization of a Stokes-Nernst-Planck-Poisson system
    In: Journal of Mathematical Analysis and Applications 390 (2012), p. 374-393
    ISSN: 0022-247X
    DOI: 10.1016/j.jmaa.2012.01.052
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2012/2012_RayMunteanKn_RigHomoOfStokesNernstPlanckPoissSystem
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  • Ray N., van Noorden T., Frank F., Knabner P.:
    Multiscale Modeling of Colloid and Fluid Dynamics in Porous Media Including an Evolving Microstructure
    In: Transport in Porous Media 95 (2012), p. 669-696
    ISSN: 0169-3913
    DOI: 10.1007/s11242-012-0068-z
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2012/2012_RayNoordenFrankKn_MultiscaleModelOfColloidAndFluidDynInPMinclAnEvolvMicrostr
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  • Buchholzer H., Kanzow C., Knabner P., Kräutle S.:
    The semismooth Newton method for the solution of reactive transport problems including mineral precipitation-dissolution reactions
    In: Computational Optimization and Applications 50 (2011), p. 193-221
    ISSN: 0926-6003
    DOI: 10.1007/s10589-010-9379-6
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2011/2011_BuchholzerKanzowKnKraeutle_TheSemismoothNewtonMethodForSolutionIncludeMineral
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  • Eck C., Garcke H., Knabner P.:
    Mathematische Modellierung
    Berlin Heidelberg: Springer, 2011
    (Springer-Lehrbuch)
    ISBN: 978-3-642-18423-9
    DOI: 10.1007/978-3-642-18424-6
    URL: http://www.springer.com/de/book/9783642184239#aboutBook
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  • Frank F., Ray N., Knabner P.:
    Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems
    In: Computing and Visualization in Science 14 (2011), p. 385-400
    ISSN: 1432-9360
    DOI: 10.1007/s00791-013-0189-0
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2011/2011_FrankRayKn_NumericalInvestiOfHomogeStokNernPlanPoissSystmes
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  • Knabner P., Ray N., Radu AF.:
    Drug release from collagen matrices and transport phenomena in porous media including an evolving microstructure
    11th Conference on Mathematical Methods in Science and Engineering (Alicante)
    In: Proceedings of the 11th International Conference on Mathematical Methods in Science and Engineering 2011
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2011/2011_KnRayRadu_DrugReleaseFromCollagMatrTranspPhenomInPMIncludAnEvolvMicrostruct
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  • Ray N., Eck C., Muntean A., Knabner P.:
    Variable Choices of Scaling in the Homogenization of a Nernst-Planck-Poisson Problem
    In: The Preprint-Series of the Institute of Applied Mathematics 344 (2011), p. 1-32
    ISSN: 1435-5833
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2011/2011_RayEckMunteanKn_VarChoiOfScalInTheHomogeniOfNernstPlanPoiProblem
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  • Suciu N., Attinger S., Radu AF., Vamo̧s C., Vanderborght J., Vereecken H., Knabner P.:
    Solute transport in aquifers with evolving scale heterogeneity
    In: The Preprint-Series of the Institute of Applied Mathematics 346 (2011), p. 1-18
    ISSN: 1435-5833
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2011/2011_SuciuAttingerRaduVamosVanderborghtVereeckenKn_SolTranspInAquifWthEvolvScaleHeterogen
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  • Suciu N., Vamo̧s C., Vereecken H., Knabner P.:
    Global Random Walk simulations for sensitivity and uncertainty analysis of passive transport models
    In: Mathematics and its Applications : Annals of the Academy of Romanian Scientists 3 (2011), p. 218-234
    ISSN: 2066-5997
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2011/2011_SuciuVamosVereeckenKn_GlobalRandomWalkSimuForSensAndUncertAnalysisOfPassiveTransModels
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  • Bause M., Hoffmann J., Knabner P.:
    First-order convergence of multi-point flux approximation on triangular grids and comparison with mixed finite element methods
    In: Numerische Mathematik 116 (2010), p. 1-29
    ISSN: 0029-599X
    DOI: 10.1007/s00211-010-0290-y
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2010/2010_BauseHoffmannKn_FirstorderConvergenceOfMultiPointFlux
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  • Carrayrou J., Hoffmann J., Knabner P., Kräutle S., de Dieuleveult C., Erhel J., Van der Lee J., Lagneau V., Mayer KU., MacQuarrie KTB.:
    Comparison of numerical methods for simulating strongly nonlinear and heterogeneous reactive transport problems-the MoMaS benchmark case
    In: Computational Geosciences 14 (2010), p. 483-502
    ISSN: 1420-0597
    DOI: 10.1007/s10596-010-9178-2
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2010/2010_CarrayrouHoffmannKnKraeutleDieuleveultErhel_ComparisonOfNumericalMethodsForSimulStrongNonlinearAndHetere
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  • Carrayrou J., Kern M., Knabner P.:
    Reactive transport benchmark of MoMaS
    In: Computational Geosciences 14 (2010), p. 385-392
    ISSN: 1420-0597
    DOI: 10.1007/s10596-009-9157-7
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2010/2010_CarrayrouKernKn_ReactiveTransportBenchmarkOfMoMaS
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  • Eck C., Jadamba B., Knabner P.:
    Error estimates for a finite element discretization of a phase field model for mixtures
    In: SIAM Journal on Numerical Analysis 47 (2010), p. 4429-4445
    ISSN: 0036-1429
    DOI: 10.1137/050637984
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2010/2010_EckJadambaKn_ErrorEstimatesForFiniteElementDiscreOfAPhaseFieldModelForMix
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  • Hoffmann J., Kräutle S., Knabner P.:
    A parallel global-implicit 2-D solver for reactive transport problems in porous media based on a reduction scheme and its application to the MoMaS benchmark problem
    In: Computational Geosciences 14 (2010), p. 421-433
    ISSN: 1420-0597
    DOI: 10.1007/s10596-009-9173-7
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2010/2010_HoffmannKraeutleKn_AParallelGlobalimplicit2DSolToTheMoMaSBenchmarkProblem
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  • Radu FA., Bause M., Knabner P., Friess W., Metzmacher I.:
    Numerical simulation of drug release from collagen matrices by Enzymatic degradation
    In: Computing and Visualization in Science 12 (2009), p. 409-420
    ISSN: 1432-9360
    DOI: 10.1007/s00791-008-0118-9
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2009/2009_RaduBauseKnFriessMetzmacher_NumericalSimulationOfDrugReleaFromCollagenMetricsByEnzymDegrad
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  • Suciu N., Knabner P.:
    Comment on "Spatial moments analysis of kinetically sorbing solutes in aquifer with bimodal permeability distribution" by M. Massabó, A. Bellin, and A. J. Valocchi
    In: Water Resources Research 45 (2009), Article No.: W05601
    ISSN: 0043-1397
    DOI: 10.1029/2008WR007498
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2009/2009_SuciuKn_CommentOnSpitalMomentsAnalysisByMassaboBerlinValocchi
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  • Suciu N., Vamo̧s C., Radu AF., Vereecken H., Knabner P.:
    Persistent memory of diffusing particles
    In: Physical Review E 80 (2009), Article No.: 061134
    ISSN: 1539-3755
    DOI: 10.1103/PhysRevE.80.061134
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2009/2009_SuciuVamosRaduVereeckenKn_PersistMemoryOfDiffParticles
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  • Hoffmann J., Kräutle S., Knabner P.:
    Computation of the MoMaS Benchmark-Problem with a Parallel Global-Implicit 2-D solver based on a Reformulation of the PDE-ODE System
    International Workshop on Modelling Reactive Transport in Porous Media (Strasbourg)
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2008/2008_HoffmannKraeutleKn_ComputOfMoMasBenchmProblWthParallGlobImplic2DsolvBasOnAReform
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  • Knabner P., Frank F., Hoffmann J., Kräutle S., Oßmann S., Prechtel A.:
    Entwicklung, Zuverlässigkeit und Effizienz reaktiver Mehrkomponententransportmodelle
    In: KORA - Synopse "Systemanalyse, Modellierung und Prognose der Wirkungen natürlicher Schadstoffminderungsprozesse - eine rezente Synopse", 2008, p. 195-233 (Gemeinsame Mitteilungen des Dresdner Grundwasserforschungszentrum e.V. und seiner Partner, Vol.5)
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  • Luckner T., Sommer T., Luckner L., Bilek F., Knabner P., Prechtel A.:
    Grundlagen der Systemanalyse, Modellierung und Prognose
    In: KORA - Synopse "Systemanalyse, Modellierung und Prognose der Wirkungen natürlicher Schadstoffminderungsprozesse - eine rezente Synopse", 2008, p. 1-81 (Gemeinsame Mitteilungen des Dresdner Grundwasserforschungszentrum e.V. und seiner Partner, Vol.5)
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2008/2008_LucknerSommerLucknerBilekKnPrechtel_GrundlagenDerSystemanalyseModellierungUndPrognose
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  • Radu AF., Pop IS., Knabner P.:
    Error estimates for a mixed finite element discretization of some degenerate parabolic equations
    In: Numerische Mathematik 109 (2008), p. 285-311
    ISSN: 0029-599X
    DOI: 10.1007/s00211-008-0139-9
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2008/2008_RaduPopKn_ErrorEstimatesForAMixedFiniteElementParabEqua
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  • Suciu N., Vamo̧s C., Vereecken H., Sabelfeld K., Knabner P.:
    Ito equation model for dispersion of solutes in heterogeneous media
    In: Revue d'Analyse Numérique et de Théorie de l'Approximation 37 (2008), p. 221-238
    ISSN: 1222-9024
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2008/2008_SuciuVamosVereeckenSabelfeldKn_ItoEquationModelForDisOfSolutesInHeteroMedia
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  • Suciu N., Vamo̧s C., Vereecken H., Sabelfeld K., Knabner P.:
    Memory effects induced by dependence on initial conditions and ergodicity of transport in heterogeneous media
    In: Water Resources Research 44 (2008), Article No.: W08501
    ISSN: 0043-1397
    DOI: 10.1029/2007WR006740
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2008/2008_SuciuVamosVereeckenSabelfeldKn_MemoryEffectsInducedByDependOnIntialCondAndErgodicity
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  • Knabner P.:
    Open Questions and Research Directions in Parameter Identification for Multicomponent Reactive Transport in Porous Media
    In: The Preprint-Series of the Institute of Applied Mathematics 315 (2007)
    ISSN: 1435-5833
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2007/2007_Kn_OpenQuestionsAndResearchDirectionsInParaIdentForMultiReactiveTransInPM
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  • Kräutle S., Knabner P.:
    A reduction scheme for coupled multicomponent transport-reaction problems in porous media: Generalization to problems with heterogeneous equilibrium reactions
    In: Water Resources Research 43 (2007), Article No.: W03429
    ISSN: 0043-1397
    DOI: 10.1029/2005WR004465
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2007/2007_KrauutleKn_AReductionSchemeForCoupledMulticomponentTransReactProbInPM
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  • Metzmacher I., Radu AF., Bause M., Knabner P., Friess W.:
    A model describing the effect of enzymatic degradation on drug release from collagen minirods
    In: European Journal of Pharmaceutics and Biopharmaceutics 67 (2007), p. 349-360
    ISSN: 0939-6411
    DOI: 10.1016/j.ejpb.2007.02.013
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2007/2007_MetzmacherRaduBauseKnFriess_ModelDescrTheEffectOfEnzymDegradOnDrugReleaseFmCollagMinirods
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  • Radu AF., Pop IS., Attinger S., Knabner P.:
    Error estimates for an Euler implicit-mixed finite element scheme for reactive transport in saturated/unsaturated soil
    In: Proceedings in Applied Mathematics and Mechanics 7 (2007), p. 1024705-1024706
    ISSN: 1617-7061
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2007/2007_RaduPopAttingerKn_ErrorEstimatesForAnEulerImplicitMIxedFiniteElementScheme
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  • Kräutle S., Knabner P., Hoffmann J.:
    Efficient and Accurate Simulation of Large General Reactive Multicomponent Transport Processes in Porous Media by Model-Preserving Decoupling Techniques
    International Conference on Computational Methods in Water Resources (Kopenhagen)
    DOI: 10.4122/1.1000000224
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2006/2006_KraeutleKnHoffmann_EfficAccurSimulOfLargeGenerReactiveMulticompTranspProcessInPMbyModelPreservDecoupTechn
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  • Prechtel A., Bitterlich S., Radu AF., Knabner P.:
    Natural Attenuation: hohe Anforderungen an die Modellsimulation Teilprojekt 6 des BayFoNA: Modellierung
    In: Grundwasser 11 (2006), p. 217-225
    ISSN: 1430-483X
    DOI: 10.1007/s00767-006-0147-6
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2006/2006_PrechtelBitterlichRaduKn_NaturalAttenuationHoheAnforderAnModellSimulation
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  • Prechtel A., Hoffmann J., Kräutle S., Knabner P.:
    Reaktive Mehrkomponentenprobleme: Sicherung von Effizienz und Zuverlässigkeit
    In: Modellierung und Prognose von Natural Attenuation-Prozessen im Untergrund, Dresden: , 2006, p. 75-90 (Gemeinsame Mitteilungen des Dresdner Grundwasserforschungszentrum e.V. und seiner Partner, Vol.3)
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2006/2006_PrechtelHoffmannKraeutleKn_ReaktiveMehrKomponentenProblemeEffizienzUndZuverlaessigkeit
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  • Radu AF., Pop IS., Knabner P.:
    Newton - Type Methods for the Mixed Finite Element Discretization of Some Degenerate Parabolic Equations
    In: Alfredo Bermúdez de Castro, Dolores Gómez, Peregrina Quintela, Pilar Salgado (ed.): Numerical Mathematics and Advanced Applications, Berlin, Heidelberg: Springer, 2006, p. 1192-1200
    ISBN: 978-3-540-34287-8

    DOI: 10.1007/978-3-540-34288-5_120
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2006/2006_RaduPopKn_NewtonTypMethFrMixedFinitElemtDiscretizOfSomeDegeneraParabolEquat
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  • Knabner P., Igler BA., Totsche KU., DuChateau P.:
    Unbiased identification of nonlinear sorption characteristics by soil column breakthrough experiments
    In: Computational Geosciences 9 (2005), p. 203-217
    ISSN: 1420-0597
    DOI: 10.1007/s10596-005-9008-0
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1997/1997_IglerTotscheKn_UnbiasIdentOfNonlinSorptCharactBySoilColumBreakthrExperim
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  • Knabner P., Kräutle S., Oßmann S., Prechtel A.:
    Modellierung des reaktiven Transports von Schadstoffen in der (un-)gesättigten Bodenzone zur Prognose der natürlichen Selbstreinigung - Komplexe Probleme berechenbar machen
    In: Dechema (ed.): Statusseminar Forschungsverbund KORA - Kontrollierter natürlicher Rückhalt und Abbau von Schadstoffen bei der Sanierung kontaminierter Grundwässer und Böden, Frankfurt a. M.: , 2005, p. 417-427
    ISBN: 389746071X

    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2005/2005_KnKraeutleOssmannPrechtel_Proj73ModellDesReaktTranspVonSchadstInDer(un)gesättBodenzonePrognSelbstreinig
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  • Kräutle S., Bause M., Prechtel A., Radu AF., Knabner P.:
    ParRichy: Parallel Simulation of Bioreactive Multicomponent Transport Processes in Porous Media
    In: Arndt Bode, Franz Durst (ed.): High Performance Computing in Science and Engineering, Garching 2004, Berlin, Heidelberg: Springer, 2005, p. 181-192
    ISBN: 978-3-540-26145-2

    DOI: 10.1007/3-540-28555-5_16
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2005/2005_KraeutleBausePrechtelRaduKn_ParRichyParallSimulOfBioreactMulticompTrnsptProcessInPM
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  • Kräutle S., Knabner P.:
    A new numerical reduction scheme for fully coupled multicomponent transport-reaction problems in porous media
    In: Water Resources Research 41 (2005), p. 1-17
    ISSN: 0043-1397
    DOI: 10.1029/2004WR003624
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2005/2005_KraeutleKn_ANewNumericalReductionSchemeForFullyCoupledMultiCompTransReactionProbInPM
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  • Suciu N., Vamos C., Knabner P., Rüde U.:
    Biased Global Random Walk, a Cellular Automaton for Diffusion
    Simulationstechnique. 18th Symposium in Erlangen. September 2005 (Erlangen)
    In: Simulationstechnique. 18th Symposium in Erlangen. September 2005, Erlangen: 2005
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2005/2005_SuciuVamosKnRuede_BiasGlobRandWalkCellAutomForDiffus
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  • Bause M., Knabner P.:
    Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods
    In: Advances in Water Resources 27 (2004), p. 565-581
    ISSN: 0309-1708
    DOI: 10.1016/j.advwatres.2004.03.005
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2004/2004_BauseKn_ComputOfVariabSaturSubsurfFlowByAdaptMixHyridFinitElemtMeth
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  • Bause M., Knabner P.:
    Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping
    In: Computing and Visualization in Science 7 (2004), p. 61-78
    ISSN: 1432-9360
    DOI: 10.1007/s00791-004-0139-y
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2004/2004_BauseKn_NumericalSimulationOfContaminaBiodegradTimeStepping
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  • Bause M., Knabner P.:
    On uniform convergence rates for Eulerian and Lagrangian finite element approximations of convection-dominated diffusion problems
    In: Calcolo 41 (2004), p. 1-26
    ISSN: 0008-0624
    DOI: 10.1007/s10092-004-0081-x
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2004/2004_BauseKn_OnUniformConvergenceRatesForEulerianLagrangianFinElemApproxOfConvDominDiffProbl
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  • Bitterlich S., Durner W., Iden S., Knabner P.:
    Inverse estimation of the unsaturated soil hydraulic properties from column outflow experiments using free-form parameterizations
    In: Vadose Zone Journal 3 (2004), p. 971-981
    ISSN: 1539-1663
    DOI: 10.2113/3.3.971
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2004/2004_BitterlichDurnerIdenKn_InverseEstimationOfTheUnsaturatedSoilHydraulPropFromColumnOutlowExperiments
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  • Bitterlich S., Knabner P.:
    Numerical methods for the determination of material properties in soil science
    In: Inverse Problems in Science and Engineering 12 (2004), p. 361-378
    ISSN: 1741-5977
    DOI: 10.1080/10682760310001597482
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2004/2004_BitterlichKn_NumericMethForDeterminOfMaterPropertInSoilScience
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  • Pop IS., Radu AF., Knabner P.:
    Mixed finite elements for the Richards' equation: Linearization procedure
    In: Journal of Computational and Applied Mathematics 168 (2004), p. 365-373
    ISSN: 0377-0427
    DOI: 10.1016/j.cam.2003.04.008
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2004/2004_PopRaduKn_MixedFiniteElementsForRichardsEquationLinearProcedure
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  • Radu AF., Pop IS., Knabner P.:
    Order of convergence estimates for an Euler implicit, mixed finite element discretization of Richards' equation
    In: SIAM Journal on Numerical Analysis 42 (2004), p. 1452-1478
    ISSN: 0036-1429
    DOI: 10.1137/S0036142902405229
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2004/2004_RaduPopKn_OrderOfConvergenceEstimatesForAnEulerImplicitMixFiniteElementDiscreRichardsEquation
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  • Schneid E., Knabner P., Radu AF.:
    A priori error estimates for a mixed finite element discretization of the Richards' equation
    In: Numerische Mathematik 98 (2004), p. 353-370
    ISSN: 0029-599X
    DOI: 10.1007/s00211-003-0509-2
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2004/2004_SchneidKnRadu_APrioriErrorEstimatesForAMixedRichardsEquation
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  • Bitterlich S., Knabner P.:
    Experimental design for outflow experiments based on a multi-level identification method for material laws
    In: Inverse Problems 19 (2003), p. 1011-1030
    ISSN: 0266-5611
    DOI: 10.1088/0266-5611/19/5/302
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2003/2003_BtterlichKn_ExpDesginForOutflowExperimentBasedOnAMultiLevelIdentification
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  • Knabner P., Angermann L.:
    Numerical Methods for Elliptic and Parabolic Partial Differential Equations
    New York: Springer, 2003
    (Texts in Applied Mathematics, Vol.44)
    ISBN: 978-0-387-95449-3
    DOI: 10.1007/b97419
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  • Knabner P., Bitterlich S., Iza Teran R., Prechtel A., Schneid E.:
    Influence of Surfactants on Spreading of Contaminants and Soil Remediation
    In: Willi Jäger, Hans-Joachim Krebs (ed.): Mathematics - Key Technology for the Future, Berlin, Heidelberg: Springer, 2003, p. 152-161
    ISBN: 978-3-642-62914-3

    DOI: 10.1007/978-3-642-55753-8_12
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2003/2003_KnBitterlichTeranPrechtelSchneid_InfluOfSurfactOnSpreadOfContaminSoilRemed
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  • Knabner P., Korotov S., Summ G.:
    Conditions for the invertibility of the isoparametric mapping for hexahedral finite elements
    In: Finite Elements in Analysis and Design 40 (2003), p. 159-172
    ISSN: 0168-874X
    DOI: 10.1016/S0168-874X(02)00196-8
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2003/2003_KnKorotovSumm_ConditionsForTheInvertOfTheIsoparaMappingForHexFiniteElements
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  • Bause M., Knabner P.:
    Uniform error analysis for Lagrange-Galerkin approximations of convection-dominated problems
    In: SIAM Journal on Numerical Analysis 39 (2002), p. 1954-1984
    ISSN: 0036-1429
    DOI: 10.1137/S0036142900367478
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2002/2002_BauseKn_UniformErrAnalysisForLangrGalerkinApproxOfConveDominaProb
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  • Bitterlich S., Knabner P.:
    Adaptive and formfree identification of nonlinearities in fluid flow from column experiments
    In: Zhangxin Chen, Richard E. Ewing (ed.): Fluid flow and transport in porous media: mathematical and numerical treatment, American Mathematical Society, 2002, p. 63-74 (Contemporary Mathematics, Vol.295)
    DOI: 10.1090/conm/295
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  • Bitterlich S., Knabner P.:
    An efficient method for solving an inverse problem for the Richards equation
    In: Journal of Computational and Applied Mathematics 147 (2002), p. 153-173
    ISSN: 0377-0427
    DOI: 10.1016/S0377-0427(02)00430-2
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2002/2002_BitterlichKn_AnEfficientMethodForSolvAnInversProbForRichardsEquation
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  • Eck C., Knabner P.:
    A Two—Scale Method for Liquid—Solid Phase Transitions with Dendritic Microstructure
    In: Michael Breuer, Franz Durst, Christoph Zenger (ed.): High Performance Scientific And Engineering Computing, Berlin, Heidelberg: Springer, 2002, p. 237-244 (Lecture Notes in Computational Science and Engineering, Vol.21)
    ISBN: 978-3-540-42946-3

    DOI: 10.1007/978-3-642-55919-8_26
    URL: http://link.springer.com/chapter/10.1007%2F978-3-642-55919-8_26
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  • Eck C., Knabner P.:
    Two-Scale Models for Liquid-Solid Phase Transitions in Binary Material with Equiaxed Microstructure
    In: Nenad Antonić, C. J. van Duijn, Willi Jäger, Andro Mikelić (ed.): Multiscale Problems in Science and Technology, Berlin, Heidelberg: Springer, 2002, p. 175-187
    ISBN: 978-3-540-43584-6

    DOI: 10.1007/978-3-642-56200-6_7
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2002/2002_EckKn_2ScaleModelsForLiquidSolidPhaseTransitInBinaryMatWithEquiaxMicrostruct
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  • Eck C., Knabner P., Korotov S.:
    A two-scale method for the computation of solid-liquid phase transitions with dendritic microstructure
    In: Journal of Computational Physics 178 (2002), p. 58-80
    ISSN: 0021-9991
    DOI: 10.1006/jcph.2002.7018
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2002/2002_EckKnKorotov_ATwoScaleMethodForTheComputationOfSolidLiquidPhaseTransitions
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  • Knabner P., Schneid E.:
    Adaptive Hybrid Mixed Finite Element Discretization of Instationary Variably Saturated Flow in Porous Media
    In: Michael Breuer, Franz Durst, Christoph Zenger (ed.): High Performance Scientific And Engineering Computing, Berlin, Heidelberg: Springer, 2002, p. 37-44 (Lecture Notes in Computational Science and Engineering, Vol.21)
    ISBN: 978-3-540-42946-3

    DOI: 10.1007/978-3-642-55919-8_4
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2002/2002_KnSchneid_AdaptHybridMixedFiniteElementDiscretiOfInstatVariablySaturFlowInPM
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  • Prechtel A., Knabner P.:
    Accurate and efficient simulation of coupled water flow and nonlinear reactive transport in the saturated and vadose zone-application to surfactant enhanced and intrinsic bioremediation
    In: S. Majid Hassanizadeh, Ruud J. Schotting, William G. Gray and George F. Pinder (ed.): Computational Methods in Water Resources, 2002, p. 687-694 (Computational Methods in Water Resources, Proceedings of the XIV International Conference on Computational Methods in Water Resources (CMWR XIV), Vol.47)
    ISBN: 978-0-444-50975-8

    DOI: 10.1016/S0167-5648(02)80125-3
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2002/2002_PrechtelKn_AccurEfficSimuOfCouplWaterFlow+nonlinReactTransp
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  • Prechtel A., Knabner P., Schneid E., Totsche KU.:
    Simulation of carrier-facilitated transport of phenanthrene in a layered soil profile
    In: Journal of Contaminant Hydrology 56 (2002), p. 209-225
    ISSN: 0169-7722
    DOI: 10.1016/S0169-7722(01)00211-X
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2002/2002_PrechtelKnSchneidTotsche_SimulationOfCarrFaciTrnasportOfPhenanInALayerSoilProfile
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  • Radu AF., Bause M., Knabner P., Lee G., Friess W.:
    Modeling of Drug Release From Collagen Matrices
    In: Journal of Pharmaceutical Sciences 91 (2002), p. 964-972
    ISSN: 0022-3549
    DOI: 10.1002/jps.10098
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2002/2002_RaduBauseKnLeeFriess_ModelingOfDrugReleaseFromCollagenMatrices
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  • Bitterlich S., Knabner P.:
    Formfree and Cascadic Identification of Material Laws in (Un)Saturated Fluid Flow from Column Experiments
    In: ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 81 (2001), p. 13-16
    ISSN: 0044-2267
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2001/2001_BitterlichKn_FormfreeAndCascadicIdentificationOfMaterialLawsL
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  • Knabner P., Korotov S., Summ G.:
    Conditions for the Invertibility of the Isoparametric Mapping for 3D Multilinear Finite Elements
    GAMM-Seminar Leipzig on Construction of Grid Generation Algorithms (Leipzig)
    In: Hackbusch W, Langer U (ed.): 17th GAMM-Seminar Leipzig on Construction of Grid Generation Algorithms 2001
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2001/2001_SummKnKorotov_CondForTheInvertibOfTheIsoparametMappFor3DmultilinFinitElem
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  • Knabner P., Summ G.:
    The invertibility of the isoparametric mapping for pyramidal and prismatic finite elements
    In: Numerische Mathematik 88 (2001), p. 661-681
    ISSN: 0029-599X
    DOI: 10.1007/PL00005454
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2001/2001_KnSumm_TheInvertibilityOfTheIsoparameForPyramidalAndPrismaticFinEle
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  • Knabner P., Tapp C., Thiele K.:
    Adaptivity in the finite volume discretization of variable density flows in porous media
    In: Physics and Chemistry of the Earth, Part B 26 (2001), p. 319-324
    ISSN: 1464-1909
    DOI: 10.1016/S1464-1909(01)00013-2
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2001/2001_KnTappThiele_AdaptivityInTheFiniteVolumeDiscretizationOfVarDensFlowsinPM
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  • Knabner P., Angermann L.:
    Numerik partieller Differentialgleichungen
    Berlin-Heidelberg: Springer, 2000
    (Springer-Lehrbuch Masterclass)
    ISBN: 978-3-540-66231-0
    DOI: 10.1007/978-3-642-57181-7
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2000/2000_BUCH_KnAngermann_NumerikPartiellerDifferentialgleichEineAnwendungsorientEinfuehrung
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  • Knabner P., Igler BA.:
    Structural Identification of Nonlinear Coefficient Functions in Transport Processes through Porous Media
    In: Hans-Joachim Bungartz, Ronald H. W. Hoppe, Christoph Zenger (ed.): Lectures on Applied Mathematics, Berlin, Heidelberg: Springer, 2000, p. 157-175
    ISBN: 978-3-642-64094-0

    DOI: 10.1007/978-3-642-59709-1_12
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2000/2000_KnIgler_StructIdentifOfNonlinCoeffFunctInTranspProcessThroughPM
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  • Knabner P., Otto F.:
    Solute transport in porous media with equilibrium and nonequilibrium multiple-site adsorption: Uniqueness of weak solutions
    In: Nonlinear Analysis - Theory Methods & Applications 42 (2000), p. 381-403
    ISSN: 0362-546X
    DOI: 10.1016/S0362-546X(98)00352-6
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2000/2000_KnOtto_SoluteTrnasInPMWithEquilibriumAndNonequilibriumMultiSiteAdsoprtion
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  • Schneid E., Prechtel A., Knabner P.:
    A comprehensive tool for the simulation of complex reactive transport and flow in soils
    In: Land Contamination and Reclamation 8 (2000), p. 357-365
    ISSN: 0967-0513
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2000/2000_SchneidPrechtelKn_AComperToolForTheSimulaOfComplexReactiveTransport
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  • De Neef MJ., Knabner P., Summ G.:
    Numerical Bifurcation Analysis of Premixed Combustion in Porous Inert Media
    In: Hans-Joachim Bungartz, Franz Durst, Christoph Zenger (ed.): High Performance Scientific and Engineering Computing, Berlin, Heidelberg: Springer, 1999, p. 39-50 (Lecture Notes in Computational Science and Engineering, Vol.8)
    DOI: 10.1007/978-3-642-60155-2_4
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1999/1999_NeefKnSumm_NumericalBifurcationAnalysisOfPremixedCombInPorInertMed
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  • Knabner P., De Neef MJ., Summ G.:
    Transient Numerical Simulation of Combustion in Inert Porous Media
    In: ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 79 (1999), p. 45-48
    ISSN: 0044-2267
    DOI: 10.1002/zamm.19990791312
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1999/1999_KnNeefSumm_TranNumSimulationOfCombInInertPM
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  • Knabner P., Summ G.:
    Hybrid Mixed Discretization Methods for Combustion Problems in Porous Media
    In: al. FK (ed.): Scientific Computing in Chemical Engineering II 1999
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1999/1999_KnSumm_HybMixDiscretMethodsForCombProbInPM
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  • Angermann L., Knabner P., Thiele K.:
    An error estimator for a finite volume discretization of density driven flow in porous media
    In: Applied Numerical Mathematics 26 (1998), p. 179-191
    ISSN: 0168-9274
    DOI: 10.1016/S0168-9274(97)00084-6
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1998/1998_AngermannKnThiele_ErrorEstimForFiniteVolDiscretOfDensDrivFlowInPM
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  • Barrett JW., Knabner P.:
    An improved error bound for a Lagrange-Galerkin method for contaminant transport with non-lipschitzian adsorption kinetics
    In: SIAM Journal on Numerical Analysis 35 (1998), p. 1862-1882
    ISSN: 0036-1429
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1998/1998_BarrettKn_ImprErrBoundForLagrGalerkMethForContTranspNonLipAdsKinet
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  • Igler BA., Totsche KU., Knabner P.:
    Identification of Nonlinear Sorption Isotherms by Soil Column Breakthrough Experiments
    In: Physics and Chemistry of the Earth 23 (1998), p. 215-219
    ISSN: 0079-1946
    DOI: 10.1016/S0079-1946(98)00016-0
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1998/1998_IglerTotscheKn_IdentOfNonlinSorpIsothBySoilColBreakthExp
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  • Knabner P., Igler BA.:
    Identification of Nonlinearities in PDEs: Sorption Isotherms in Reactive Flow Through Porous Media
    ENUMATH 97 (Singapore)
    In: Bock H (ed.): ENUMATH 97, World Scientific, Singapore 1998
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1998/1998_IglerKn_IdentifOfNonlinearitInPDEsSorptIsothermInReactFlowThroughPM
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  • Knabner P., Tapp C., Thiele K.:
    Adaptive Finite Volume Discretization of Density Driven Flows in Porous Media
    In: Acta Mathematica Universitatis Comenianae 67 (1998), p. 115-136
    ISSN: 0862-9544
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1998/1998_KnTappThiele_AdFinVolDiscretOfDensDrivFlowsInPM
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  • Knabner P., Van Duijn CJ(., Schotting RJ.:
    An analysis of crystal dissolution fronts in flows through porous media part 2: incompatible boundary conditions
    In: Advances in Water Resources 22 (1998), p. 1-16
    ISSN: 0309-1708
    DOI: 10.1016/S0309-1708(97)00038-9
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1998/1998_DuijnKnSchotting_AnalysCrystDissolFroInFlowThrPMPart2IncompBoundCondi.pdf
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  • Lührmann L., Fein E., Knabner P.:
    A case study on the influence of sorption inhomogeneities on the migration of contaminants
    In: Environmental Sciences (B3110), INIS, 1998, p. 317-326
    ISBN: 92-64-16099-X

    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1997/1997_LuehrmannFeinKn_CaseStudyOnTheInfluenOfSorptInhomogenOnMigrationOfContaminants
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  • Lührmann L., Klotz D., Knabner P.:
    Modellierung des kolloidgetragenen Stofftransports angewandt auf Eu-Humat-Migrationsexperimente
    Uranium Mining and Hydrogeology II (Freiberg, 15-09-1998 - 17-09-1998)
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1998/1998_LuehrmannKlotzKnNoseck_ModellierDesKolloidgetrStofftrnspAngewAufEuHumatMigrationsex
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  • Barrett JW., Kappmeier H., Knabner P.:
    Lagrange-Galerkin Approximation For Advection-Dominated Contaminant Transport With Nonlinear Equilibrium Or Non-equilibrium Adsorption
    In: Rainer Helmig, Willi Jäger, Wolfgang Kinzelbach, Peter Knabner, Gabriel Wittum (ed.): Modeling and Computation in Environmental Sciences, Braunschweig, Wiesbaden: Vieweg+Teubner, 1997, p. 36-48 (Notes on Numerical Fluid Mechanics, Vol.59)
    DOI: 10.1007/978-3-322-89565-3_4
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1997/1997_BarrettKappmeierKn_LagrangeGalerkinApproxWithNonlinearNonequilibAdsorption
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  • Barrett JW., Knabner P.:
    Finite Element Approximation of the Transport of Reactive Solutes in Porous Media. Part 1: Error Estimates for Nonequilibrium Adsorption Processes
    In: SIAM Journal on Numerical Analysis 34 (1997), p. 201-227
    ISSN: 0036-1429
    DOI: 10.1137/S0036142993249024
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1997/1997_BarrettKn_FinEleApprOfTranspOfReactSolutInPMPart1
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  • Barrett JW., Knabner P.:
    Finite element approximation of the transport of reactive solutes in porous media. part II: Error estimates for equilibrium adsorption processes
    In: SIAM Journal on Numerical Analysis 34 (1997), p. 455-479
    ISSN: 0036-1429
    DOI: 10.1137/S0036142993258191
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1997/1997_BarrettKn_FinEleApprOfTranspOfReactSolutInPMPart2
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  • Knabner P., Igler BA., Kappmeier H., Schneid E., Hempfling R.:
    Trägerbeeinflußter und lösungsvermittelter Transport von Umweltchemikalien in porösen Medien
    In: Karl-Heinz Hoffmann, Willi Jäger, Thomas Lohmann, Hermann Schunck (ed.): Mathematik Schlüsseltechnologie für die Zukunft, Berlin, Heidelberg: Springer, 1997, p. 231-241
    DOI: 10.1007/978-3-642-60550-5_20
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1997/1997_IglerKappmeierSchneidKnHempfling_TraegerUndLoesungsverTransportVonUmweltchemikalienInPM
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  • Knabner P., Schneid E.:
    Numerical Solution of Unsteady Saturated/Unsaturated Flow Through Porous Media
    In: Numerical Modelling in Continuum Mechanics, Part II 1997
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1997/1997_KnSchneid_NumericSolOfUnsteadySatUnsatFlowThrPM
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  • Van Duijn CJ(., Knabner P.:
    Travelling wave behaviour of crystal dissolution in porous media flow
    In: European Journal of Applied Mathematics 8 (1997), p. 49-72
    ISSN: 0956-7925
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1997/1997_DuijnKn_TravWaveBehavOfCrystDissInPMflow
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  • Knabner P., Frolkovic P.:
    Consistent Velocity Approximations in Finite Element or Volume Discretizations of Density Driven Flow
    In: Computational Methods in Water Resources, Computational Mechanics Publication, Southampton, 1996, p. 93–100
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1996/1996_KnFrolkovic_ConsVeloApprForFinVolOrElemtDiscrOfDensDrivFlowInPM
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  • Knabner P., Schneid E.:
    Qualitative Properties of a Model for Carrier Facilitated Groundwater Contaminant Transport
    In: Frerich Keil, Wolfgang Mackens, Heinrich Voß, Joachim Werther (ed.): Scientific Computing in Chemical Engineering, Berlin, Heidelberg: Springer, 1996, p. 129-135
    ISBN: 978-3-642-80151-8

    DOI: 10.1007/978-3-642-80149-5_14
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1996/1996_KnSchneid_QualPropOfAModelForCarrierFaciliGroundwaterContTrans
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  • Knabner P., Totsche KU., Kögel-Knabner I.:
    The modeling of reactive solute transport with sorption to mobile and immobile sorbents. 1. Experimental evidence and model development
    In: Water Resources Research 32 (1996), p. 1611-1622
    ISSN: 0043-1397
    DOI: 10.1029/95WR02994
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1996/1996_KnTotscheKoegelkn_ModelOfReactSolutTranspWthsorptToMobImmobSorbP1
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  • Totsche KU., Knabner P., Kögel-Knabner I.:
    The modeling of reactive solute transport with sorption to mobile and immobile sorbents. 2. Model discussion and numerical simulation
    In: Water Resources Research 32 (1996), p. 1623-1634
    ISSN: 0043-1397
    DOI: 10.1029/95WR02993
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1996/1996_KnTotscheKoegelkn_ModelOfReactSolutTranspWthsorptToMobImmobSorbP2
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  • Van Duijn CJ(., Knabner P.:
    Crystal dissolution in porous media flow
    In: ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 76 (1996), p. 329-332
    ISSN: 0044-2267
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1996/1996_DuijnKn_CrystDissolInPMFlow
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  • Barrett JW., Knabner P.:
    Analysis and Finite Element Approximation of Transport of Reactive Solutes in Porous Media
    In: Alain Bourgeat et al. (ed.): Mathematical Modelling of Flow through Porous Media 1995
    BibTeX: Download
  • Knabner P., Van Duijn CJ(., Hengst S.:
    An analysis of crystal dissolution fronts in flows through porous media. Part 1: Compatible boundary conditions
    In: Advances in Water Resources 18 (1995), p. 171-185
    ISSN: 0309-1708
    DOI: 10.1016/0309-1708(95)00005-4
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1995/1995_KnDuijnHengst_AnalysOfCrystDissolFroInFlowsThPM Part1CompBoundCond
    BibTeX: Download

  • Knabner P., Barrett JW., Kappmeier H.:
    Lagrange-Galerkin Approximation of Advection-Dominated Nonlinear Contaminant Transport in Porous Media
    In: Computational Methods in Water Resources, 1994, p. 299-308
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1994/1994_KnBarrettKappmeier_LagrGalApprxOfAdvectDominNonlinContamTrspInPM
    BibTeX: Download
  • Van Duijn CJ(., Knabner P.:
    Flow and reactive transport in porous media induced by well injection: Similarity solution
    In: IMA Journal of Applied Mathematics 52 (1994), p. 177-200
    ISSN: 0272-4960
    DOI: 10.1093/imamat/52.2.177
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1994/1994_DuijnKn_FlwReactTrnspInPMInducedByWellInjectSimSol
    BibTeX: Download

  • Knabner P., Kögel-Knabner I., Totsche KU.:
    CARRIER INFLUENCED TRANSPORT OF POLLUTANTS IN POROUS MEDIA: MATHEMATICAL MODELLING
    In: Contaminated Soil '93, Dordrecht: Springer, 1993, p. 163-172 (Soil and Environment, Vol.2)
    ISBN: 978-94-010-4892-7

    DOI: 10.1007/978-94-011-2018-0_31
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1993/1993_KnKoegelknabTotsche_CarrInfluencedTransOfPollutantsInPM
    BibTeX: Download
  • Van Duijn CJ(., Knabner P., van der Zee SEATM.:
    Travelling waves during the transport of reactive solute in porous media: Combination of Langmuir and Freundlich isotherms
    In: Advances in Water Resources 16 (1993), p. 97-105
    ISSN: 0309-1708
    DOI: 10.1016/0309-1708(93)90001-V
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1993/1993_DuijnKnZee_TravlWaveDurTrspOfReactSoluteInPMCombOfLangFreundl
    BibTeX: Download

  • Friedmann A., Knabner P.:
    A Transport Model with Micro- and Macro-Structure
    In: Journal of Differential Equations 98 (1992), p. 328-354
    ISSN: 0022-0396
    DOI: 10.1016/0022-0396(92)90096-6
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1992/1992_FriedmannKn_TrnspModelWithMicroAndMacroStruct
    BibTeX: Download
  • Knabner P.:
    Finite-Element-Approximation of Solute Transport in Porous Media with General Adsorption Processes
    In: Gilding Brian Howard, Hornung Ulrich, Van Duijn C J (ed.): Flow And Transport In Porous Media - Proceedings Of The Summer School, World Scientific, 1992, p. 223-292
    ISBN: 9814507334, 978981450733

    DOI: 10.1142/9789814368438_0003
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1991/1991_Kn_FinElemApproxOfSolTranspInPMwthGenAdsorptProcesses
    BibTeX: Download
  • van Duijn CH., Knabner P.:
    Travelling Waves in the Transport of Reactive Solutes through Porous Media: Adsorption and Binary Ion Exchange - Part 1
    In: Transport in Porous Media 8 (1992), p. 167-194
    ISSN: 0169-3913
    DOI: 10.1007/BF00617116
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1992/1992_DuijnKn_TravellingWavesThroughPMAdsorptionPart1
    BibTeX: Download
  • van Duijn CH., Knabner P.:
    Travelling Waves in the Transport of Reactive Solutes through Porous Media: Adsorption and Binary Ion Exchange - Part 2*
    In: Transport in Porous Media 8 (1992), p. 199-225
    ISSN: 0169-3913
    DOI: 10.1007/BF00618542
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1992
    BibTeX: Download

  • Hoffmann KH., Knabner P., Seifert W.:
    Adaptive Methods for Parameter Identification in Ground Water Hydrology
    In: Advances in Water Resources 14 (1991), p. 220-239
    ISSN: 0309-1708
    DOI: 10.1016/0309-1708(91)90036-N
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1991/1991_HoffmannKnSeifert_AdaptMethForParamIdentInGrndWatHydrology
    BibTeX: Download
  • Knabner P.:
    Mathematische Modelle für Transport und Sorption gelöster Stoffe in porösen Medien
    Peter Lang, 1991
    (Methoden und Verfahren der mathematischen Physik)
    ISBN: 9783631437186
    BibTeX: Download
  • Knabner P., Seifert W.:
    Das Finite-Element-Programm FELIPE: Programmbeschreibung und Benutzerhandbuch, Version 1.2
    Augsburg, 1991
    BibTeX: Download
  • Knabner P., Wolfersdorf Lv.:
    Travelling Wave Solutions of a System of Nonlinear Diffusion Equations with Integral Term
    In: Zeitschrift für Analysis und ihre Anwendungen 10 (1991), p. 503-512
    ISSN: 0232-2064
    DOI: 10.4171/ZAA/471
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1991/1991_KnWolfersdorf_TrvlWaveSolOfASystOfNonlinDiffusEquaWthIntegrTerm
    BibTeX: Download
  • Kögel-Knabner I., Knabner P., Deschauer H.:
    Dissolved Organic Matter as Carrier for Exogenous Organic Chemicals in Soils
    In: W.S. Wilson (ed.): Advances in Soil Organic Matter Research, Woodhead Publising Ltd., 1991, p. 121-128
    ISBN: 978-1-85573-813-3

    DOI: 10.1016/B978-1-85573-813-3.50016-0
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1991/1991_KoegelknKnDeschauer_DissolOrganMattAsCarrFrExogenOrgChemicInSoils
    BibTeX: Download
  • van Duijn CH., Knabner P.:
    Solute Transport in porous media with equilibrium and non-equilibrium multiple-site adsorption: Travelling waves
    In: Journal für die reine und angewandte Mathematik 1991 (1991), p. 1-50
    ISSN: 0075-4102
    DOI: 10.1515/crll.1991.415.1
    BibTeX: Download

  • Kögel-Knabner I., Knabner P., Deschauer H.:
    Enhanced Leaching of Organic Chemicals in Soils due to Binding to Dissolved Organic Carbon?
    In: F. Arendt, M. Hinsenveld, W. J. Van Den Brink (ed.): Contaminated Soil '90, Dordrecht: Springer, 1990, p. 323-329
    ISBN: 978-94-010-5443-0

    DOI: 10.1007/978-94-011-3270-1_72
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1990/1990_KoegelknKnDeschauer_EnhancLeachOfOrganChemicInSoilsDueToBindToDissolvOrganCarbon
    BibTeX: Download

  • Knabner P., Vessella S.:
    The Optimal Stability Estimate for some Ill-posed Cauchy Problems for a Parabolic Equation
    In: Mathematical Methods in the Applied Sciences 10 (1988), p. 575-583
    ISSN: 0170-4214
    DOI: 10.1002/mma.1670100507
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1988/1988_KnVessella_TheOptimStabilEstimForSomeIllposedCauchyProblForAParabolEquation
    BibTeX: Download

  • Knabner P.:
    Finite Element Simulation of Saturated-Unsaturated Flow through Porous Media
    In: P. Deuflhard B. Engquist (ed.): Large Scale Scientific Computing, Boston: Birkhäuser, 1987, p. 83-93 (Progress in Scientific Computing, Vol.7)
    ISBN: 978-1-4684-6756-7

    DOI: 10.1007/978-1-4684-6754-3_6
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1987/1987_Kn_FinitElementSimulOfSaturUnsaturFlowThroughPM
    BibTeX: Download
  • Knabner P., Vessella S.:
    Stability Estimates for Ill-Posed Cauchy Problems for Parabolic Equations
    In: Heinz W. Engl and C.W. Groetsch (ed.): Inverse and Ill-posed Problems, Academic Press, 1987, p. 351-368 (Inverse and Ill-Posed Problems, Vol.4)
    ISBN: 978-0-12-239040-1

    DOI: 10.1016/C2013-0-10621-6
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1987/1987_KnVessella_StabilityEstimatesForIIIPosedCauchyProblForParabolEqua
    BibTeX: Download
  • Knabner P., Vessella S.:
    Stabilization of Ill-Posed Cauchy Problems for Parabolic Equations
    In: Annali Di Matematica Pura Ed Applicata 149 (1987), p. 393-409
    ISSN: 0373-3114
    DOI: 10.1007/BF01773944
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1987/1987_KnVessella_StabilizationOfIllPosedCauchyProblemsForParaEquation
    BibTeX: Download

  • Knabner P.:
    A Free Boundary Problem Arising from the Leaching of Saline Soils
    In: SIAM Journal on Mathematical Analysis 17 (1986)
    ISSN: 0036-1410
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1986/1986_Kn_FreeBoundProblmArisFmTheLeachOfSalineSoils
    BibTeX: Download
  • Knabner P.:
    Global Existence in a General Stefan-like Problem
    In: Journal of Mathematical Analysis and Applications (1986), p. 543-559
    ISSN: 0022-247X
    Open Access: https://core.ac.uk/download/pdf/82198033.pdf
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1986/1986_Kn_GlobalExistInAGenStefanLikeProblm
    BibTeX: Download

  • Knabner P.:
    Control of Stefan Problems by Means of Linear-Quadratic Defect Minimization
    In: Numerische Mathematik 46 (1985), p. 429-442
    ISSN: 0029-599X
    DOI: 10.1007/BF01389495
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1985/1985_Kn_ControlOfStefanProblemsByMeansLinearQuadraticDefMini
    BibTeX: Download

  • Knabner P.:
    Regularization of the Cauchy Problem for the Heat Equation by Norm Bounds
    In: Applicable Analysis, London: Gordon and Breach Science Publishers, Inc., 1984, p. 295-311
    DOI: 10.1080/00036818408839503
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1984/1984_Kn_RegularizOfTheCauchyProblForTheHeatEquatByNormBounds
    BibTeX: Download

  • Knabner P.:
    Regularizing the Cauchy Problem for the Heat Equation by Sign Restrictions
    In: Improperly Posed Problems and Their Numerical Treatment, Basel: Birkhäuser, 1983, p. 165-177 (International Series of Numerical Mathematics, Vol.63)
    ISBN: 978-3-0348-5462-7

    DOI: 10.1007/978-3-0348-5460-3_12
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1983/1983_Kn_RegularizingTheCauchyProblForTheHeatEquatiBySignRestrict
    BibTeX: Download
  • Knabner P.:
    Stability Theorems for General Free Boundary Problems of the Stefan Type and Applications
    In: Rudolf Gorenflo, Karl-Heinz Hoffmann (ed.): Applied nonlinear Functional Analysis, Frankfurt am Main: Verlag Peter Lang, 1983 (Methoden und Verfahren der mathematischen Physik, Vol.25)
    ISBN: 3820472975, 9783820472974

    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1982/1982_Kn_StabilityTheoremsForGenFreeBoundProblOfTheStefanTypeAndAppl
    BibTeX: Download

  • Knabner P.:
    Das inverse Stefan Problem - Ein Vergleich verschiedener Fragestellungen
    In: J. Albrecht, L. Collatz, K.-H. Hoffmann (ed.): Numerische Behandlung freier Randwertaufgaben, Basel: Birkhäuser Verlag, 1982, p. 145-160 (International Series of Numerical Mathematics, Vol.58)
    ISBN: 978-3-0348-6565-4

    DOI: 10.1007/978-3-0348-6563-0_11
    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1982/1982_Kn_DasinverseStefanProblemEinVerglVerschFragestellungen
    BibTeX: Download

  • Hoffmann KH., Knabner P.:
    Freie Randwertprobleme
    In: Prof. Dr. Günter Meinardus (ed.): Approximatiion in Theorie und Praxis, Mannheim: Bibliographisches Institut, 1979
    ISBN: 3411015675

    URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_1979/1979_HoffmannKn_FreieRandwertprobleme
    BibTeX: Download

Projects

  • Interfaces, complex structures, and singular limits in continuum mechanics


    (Third Party Funds Group – Overall project)
    Term: 01-04-2018 - 30-09-2022
    Funding source: DFG / Graduiertenkolleg (GRK)
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  • MPFA and MHFE methods for flow and transport in porous media


    (Third Party Funds Single)
    Term: 01-01-2012 - 31-12-2013
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)
    Abstract

    Nonlinear (multiphase) flow and reactive multicomponent transport problems in highly heterogeneous porous media and their numerical simulation are of great interest for evaluating site remediation, energy exploitation or CO2 sequestration scenarios.   The resulting advection-diffusion-reaction-systems are coupled nonlinear parabolic partial differential equations, and we have parabolic or elliptic nonlinear flow equations, possibly degenerate. The development of convergent and efficient numerical schemes is very challenging and the mixed (hybrid) finite element method M(H)FEM and the multipoint flux approximation MPFA are powerful locally mass conservative choices. They offer also the advantage of continuous flux approximations over the element faces.  Analogies between the two techniques should help to prove order of convergence estimates and monotonicity for the multicomponent transport problems, but also for multiphase flow.  Furthermore numerical diffusion of the schemes should be quantified to assess the accuracy of the methods.  Simulation examples should include realistic scenarios on heterogeneous, log normally distributed random parameter fields.

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  • Development of filtration systems for air cleaning from nanoparticles, organic admixtures and bacteria with the help of numerical simulations


    (Third Party Funds Single)
    Term: 01-10-2009 - 30-09-2011
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)
    Abstract

    The project was a cooperation of a group of applied mathematicians with the Russian company Aeroservice for the development and optimization of new photocatalytic filter systems for air cleaning of nanoparticles and organic substances with the help of mathematical simulation tools. For the simulation of aerosol transport in the filter made of polypropylene fibers, which is used in hospitals or airports, e.g., mathematical models and efficient solution algorithms had to be developed. These allow on the one hand to take stochastic components into account, as the heterogeneous conductivity distribution in the filter. On the other hand these methods were coupled with highly accurate computation schemes as mixed finite element methods, which guarantee local mass conservation for the transport processes. The design parameters of real experiments can be optimized with the help of such simulation tools and their sensitivity with respect to filter efficiency analysed. Among the used methods are particle filtration in porous media, based on the Darcy equation, and coupled Eulerian and Lagrangeian simulation of transport processes, including Monte Carlo approaches with given filter geometries.

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  • Efficient Numerical Methods for Large Partial Differential Complementarity Systems arising in Multispecies Reactive Transport with Minerals in Porous Media


    (Third Party Funds Single)
    Term: 01-01-2007 - 31-12-2011
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    Abstract
    The project focuses on the accurate and efficient numerical treatment of time-dependent reactive transport problems with many species (in porous media) in 2 or 3 space dimensions with local complementarity conditions as essential ingredient. The problem takes the form of a differential algebraic set of equations and complementarity constraints, consisting of time dependent (possibly convection-dominated) semilinear partial differential equations (PDEs), nonlinear ordinary differential equations, nonlinear algebraic equalities, and inequalities. Taking a typical species number of 10 to 20 and of nodal degrees of freedom of 104 to 106, also for an appropriate (e.g., local mass conservative) discretization, the solution of the emerging finite dimensional complementarity system is a formidable task, whose efficient algorithmic treatment is the main topic of the project. Algorithms of semismooth Newton type are the principal choice. Aims are the investigation and improvement of the algorithms w.r.t. efficiency and robustness, and comparing them to other (e.g., interiorpoint-) methods. The algorithms to be developed are supposed to heavily take advantage of knowledge about the substructuring of the problem. The emerging methods and software, also for parallel computers, is supposed to handle several large real world problems, not yet treatable satisfactorily.
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  • The Influence of Colloids on Water Flow and Solute Transport in Soils: Side Effect or Key Process?


    (Third Party Funds Single)
    Term: 01-11-2006 - 31-12-2009
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    Abstract

    Soil colloids may influence the interaction between solutes and the immobile solid phase. A coupling to the fluid transport is possible by processes of sedimentation, flocculation, precipitation, filtration and deposition. The objective of this research project is the qualitative and quantitative examination of the crucial aspects of colloidal-influenced solute- and fluid transport by means of systematic, prognostic simulation. In detail,

    1. the attachment and detachment of colloids under consideration air-water interface of the soil,
    2. the transformation of the pore space and the thus induced coupling to the fluid transport in soil, and
    3. the transformation of the surface properties of the solid phase and the thus induced coupling to the solute transport

    have to be analyzed. The main hypothesis of this project states that the couplings incorporated in the model conception affect the praxis-relevant situations not only qualitatively, but also quantitatively in a significant way. The deterministic description of the physicochemical mechanisms on basis of the conservation laws for mass, impulse and energy results in systems of time-dependent non-linear partial differential equations. In order to make the model operative with respect to the problem formulation, one has to approximate it via numerical methods and to implement those in a software tool. For each level of complexity which has to be achieved, a comparison with existing experimental data has to be accomplished. In particular, these datasets have is to be used to obtain a realistic parametrization of the model via inverse modelling.

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  • Identifizierung nichtlinearer Koeffizientenfunktionen des reaktiven Transports durch poröse Medien unter Verwendung rekursiver und formfreier Ansätze


    (Third Party Funds Group – Sub project)
    Overall project: Identifikation, Optimierung und Steuerung für technische Anwendungen
    Term: 01-06-2006 - 30-04-2010
    Funding source: Bayerisches Staatsministerium für Bildung und Kultus, Wissenschaft und Kunst (ab 10/2013)
    Abstract

    In dem Internationalen Doktorandenkolleg wird vor dem Hintergrund konkreter Anwendungsprobleme der Bogen von der mathematischen Modellierung über die mathematische Analyse und die Entwicklung numerischer Methoden bis hin zum Wissenschaftlichen Rechnen und der Implementierung von Software auf Hoch- und Höchstleistungsrechnern gespannt. Dies geschieht auf den Gebieten der Identifikation, Optimierung und Steuerung komplexer technischer, medizinischer, naturwissenschaftlicher und wirtschaftswissenschaftlicher Systeme.

    Identifikation, Optimierung und Steuerung haben eine große Bedeutung für die technologische Entwicklung. Die Fokussierung auf dieses Gebiet ist deshalb das besondere Merkmal dieses mathematisch orientierten Netzwerkes. Im nordbayerischen Raum bieten sich wegen der dort gegebenen Konzentration international anerkannter Wissenschaftler in diesem Forschungsumfeld die besten Voraussetzungen. Das Ziel des Doktorandenkollegs ist es, den Schritt von der modellbasierten Simulation zum modellgestützten optimalen Design und Steuerung zu vollziehen. Dieser Schritt wird erst durch die Verzahnung der rasanten Entwicklung mathematischer Methoden der Optimierung und der Numerik und mit Hilfe von Hochleistungsrechnern möglich.

    Eine stärkere Einbindung von Ingenieurprojekten in der zweiten Phase des Kollegs wird die Integration der erarbeiteten Konzepte und Algorithmen in konkrete Anwendungsbereiche ermöglichen. Darüber hinaus lassen spezifische Betreuungs- und Lehrkonzepte die fachübergreifende Zusammenarbeit fruchtbar werden.
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  • Modelling of the reactive transport of contaminants in the (un-)saturated zone for the prognosis of natural attenuation


    (Third Party Funds Group – Sub project)
    Overall project: Kontrollierter natürlicher Rückhalt und Abbau von Schadstoffen bei der Sanierung kontaminierter Böden und Grundwässer (BMBF Förderschwerpunkt KORA)
    Term: 01-04-2004 - 31-12-2008
    Funding source: BMBF / Verbundprojekt
    Abstract

    The evaluation of the potential of contaminated sites concerning natural attenuation needs comprehensive process descriptions and accurate, reliable numerical algorithms. Numerical errors may lead to qualitatively completely wrong conclusions concerning the potential of the site for degradation. It has been developed a comprehensive and flexible simulation tool, that is outstanding concerning the variety of processes, the quality and efficiency of the calculations ensured by modern numerical methods as well as the usability. The existing software platform RICHY has been extended, which is already intensely and successfully used by universities, institutes and consultants for the simulation of reactive transport and parameter identification. Among previous modules for coupled sufactant transport, preferential, unsaturated flow or carrier facilitated transport the project could realize new model components that surpass most of all existing software packages. The extensions contain complete descriptions of microbially catalysed degradation with arbitrary reaction partners and inhibition, general multicomponent reactions including the effects of ionic strength, as well as mineral dissolution and precipitation. The efficient and highly accurate, newly developed mathematical solution algorithms for the resulting coupled systems of partial differential equations could show their quality in complex international benchmark studies. Locally mass conserving, mixed hybrid finite element discretisations of the flow problem have been combined with globally implicit, reactive multicomponent models. Novel reduction methods for the latter rely on the linear transformation of the equation systems and variables and lead to the consideration of conservation quantities which can be handled efficiently, as a part of the transport – reaction – equations decouples. Another approach that has been pursued simultaneously relies on a modified Newton method and results in efficiency enhancements by the neglection of coupling terms in the Jacobian matrix. This algorithm can be applied fully adaptively, in 1D as well as in 2D. Both approaches could be combined with adaptive techniques for the automatic, efficient choice of time steps and spatial grid sizes, which makes the calculation of these complex problems feasible on PCs.

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  • Development of a simulation tool for the prognosis of the spreading and the degradation of contaminants in the saturated and vadose zone


    (Third Party Funds Group – Sub project)
    Overall project: Nachhaltige Altlastenbewältigung unter Einbeziehung des natürlichen Reinigungsvermögens
    Term: 01-06-2001 - 31-05-2003
    Funding source: Bayerisches Staatsministerium für Umwelt und Gesundheit (StMUG) (bis 09/2013)
    URL: https://www.altlasten-bayern.de/projekte/verbundvorhaben-na/
    Abstract

    The project included the mathematical modelling of natural attenuation processes in the subsurface and the extension of a software tool for complex reactive multicomponent processes in the framework of mixed hybrid and conforming finite elements. New  parameter identification methods allow the parametrization of unknown functions or a formfree optimization, and help to overcome the dilemma of missing data in complex models. Work included instationary 3D simulations and scenarios of  contaminated sites explored by project partners. The findings of the joint research project resulted in guidelines for authorities and consulting engineers dealing with natural attenuation at contaminated sites.

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  • Quantification of Contaminant Sources and Transport Prognosis in Aquifers


    (Third Party Funds Group – Sub project)
    Overall project: BMBF Förderschwerpunkt Sickerwasserprognose
    Term: 01-01-2001 - 31-12-2004
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)
    Abstract

    Mathematical simulation tools allow the quantitative integration of competing transport and transformation processes which are relevant for a seepage water risk prognosis. Therefore model simulations have to contain a comprehensive process description, while they can serve for parameter identification by inverse modelling of suitable column or batch experiments, and allow to quantify the dependence of a key variable on parameters through a simultaneous sensitivity analysis. The software platform RICHY1D has been extended and is already intensively and successfully used in universities, institutes and by consultants for the 1D simulation of complex reactive transport and for parameter identification. It stands out by the application of efficient and highly accurate mathematical solution strategies for the resulting systems of partial differential equations (e.g. locally mass conserving mixed hybrid finite element discretisations, modified Newton’s method). Besides the formerly existing modules for coupled surfactant-water transport, multiphase flow, saturated-unsaturated flow or carrier facilitated transport, the extensions contain in particular source terms (boundary conditions, distributed sources, arbitrarily time dependent, nonlinear and multiple (de-)sorption kinetics, mobilisation from a residual NAPL phase), preferential flow with solute transport, and heat transport in soils with coupling to reaction parameters of the contaminant transport like Monod degradation parameters, e.g.. The parameter identification is possible for the model extensions as well, which allows the identification of multiple complex parametrizations from suitable experiments (for example for source terms or microbially mediated degradation, sorption characteristics and hydraulic parameters). There is no need to impose a certain functional shape of these nonlinearities, the so-called form-free identification is also feasible, and furthermore a closed-flow experiment design can be accounted for. The sensitivity analysis is provided separately for the evaluation of the dependence of a key variable like the concentration of arbitrary model parameters, what represents a powerful tool in a transport simulation to identify controlling factors and evaluate uncertainties of the data.

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