On fully practical finite element approximations of degenerate Cahn-Hilliard systems
Department of Mathematics, Imperial College, London, SW7 2BZ, UK. (firstname.lastname@example.org)
2 Department of Mathematical Sciences, University of Durham, DH1 3LE, UK.
3 Institut für Angewandte Mathematik, Wegelerstraße 6, 53115 Bonn, Germany.
We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments with three components in one and two space dimensions are presented.
Mathematics Subject Classification: 35K35 / 35K55 / 35K65 / 65M12 / 65M60 / 82C26
Key words: Phase separation / multi-component systems / degenerate parabolic systems of fourth order / finite element method / convergence analysis.
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