A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions
A finite element space semi-discretization of the Cahn-Hilliard equation with dynamic boundary conditions has been studied. Optimal error estimates in energy and weaker norms have been proved for sufficiently regular solutions. A convergence result in a weak sense for less regular solutions has also been proved. A fully discrete scheme based on the backward Euler scheme for the time discretization has been proposed and proved to be unconditionally stable. Some numerical examples are presented.
scientific article; zbMATH DE number 5725445