On contact angles and boundary layers: Dynamic boundary conditions for
Vortragender: Stefan Metzger, FAU; Habilitationsvortrag
Important qualitative features of two-phase systems related to phase separation
processes can be described by Cahn-Hilliard equations. For these equations, many
different boundary conditions are available. While the simplest boundary
conditions dictate a static contact angle and prevent flux across the boundary,
more sophisticated models use additional partial differential equations to
describe effects like dynamic contact angles or the presence of a boundary layer.
In this talk, we will discuss the numerical treatment of Cahn-Hilliard-type
dynamic boundary conditions that were introduced in the recent years to
approximate boundary layers (cf. Goldstein, Miranville, Schimperna, Physica D,
2011; Liu, Wu, Arch. Ration. Mech. Anal., 2019; Knopf, Lam, Liu, M., M2AN,
2021). From the mathematical point of view, all of these models describe
evolutions, which minimize Ginzburg-Landau-type free energies in the bulk and on
the surface, but differ in the considered adsorption processes.
We will present a fully discrete linear finite element scheme based on the
scalar auxiliary variable approach. Using that this discretization is
unconditionally stable w.r.t. a modified energy, we are able to establish a
convergence result and thereby also guarantee the existence of weak solutions to
the original problem.