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A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions. (English) Zbl 1204.65113
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.

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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