A numerical analysis of the cahn-hilliard equation with dynamic boundary conditions

Abstract

We consider a finite element space semi-discretization of the CahnHilliard equation with dynamic boundary conditions. We prove optimal error estimates in energy norms and weaker norms, assuming enough regularity on the solution. When the solution is less regular, we prove a convergence result in some weak topology. We also prove the stability of a fully discrete problem based on the backward Euler scheme for the time discretization. Some numerical results show the applicability of the method.