PDEs on diffuse interfaces with applications to two-phase flow
Charles M. Elliott, Björn Stinner · 2011
We have been developing and analysing an approach to solve an advection diffusion equations on a moving hypersurface represented by a thin layer. A suitable bulk density approximating the surface is employed to formulate the problem but leads to degenerate coeffcients which makes the analysis, convergence as the layer thickness tends to zero, and performing computations challenging. Our numerical method is based on linear finite elements and allows for an easy coupling with, for instance, phase field models describing the motion of the interface. Exemplary, we consider a simple model for two-phase ow with surfactants where the double-obstacle potential is used in order to ensure a finite interfacial thickness.