Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility. (English) Zbl 1126.65321
Summary: We consider the Cahn-Hilliard equation with a logarithmic free energy and non-degenerate concentration dependent mobility. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Further, we prove an error bound for a fully practical piecewise linear finite element approximation in one and two space dimensions. Finally some numerical experiments are presented.
MSC:
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
35K55 | Nonlinear parabolic equations |
35K35 | Initial-boundary value problems for higher-order parabolic equations |
82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |