On Fully Practical Finite Element Approximations of Degenerate Cahn-Hilliard Systems

Barrett, J.W.; Blowey, J.F.; Garcke, H.

Abstract

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.

Citation

Barrett, J., Blowey, J., & Garcke, H. (2001). On Fully Practical Finite Element Approximations of Degenerate Cahn-Hilliard Systems. ESAIM: Mathematical Modelling and Numerical Analysis, 35(4), 713-748. https://doi.org/10.1051/m2an%3A2001133

• Journal Article Type: Article
• Publication Date: Jul 1, 2001
• Deposit Date: Apr 24, 2007
• Publicly Available Date: May 17, 2010
• Journal: ESAIM: Mathematical Modelling and Numerical Analysis
• Print ISSN: 0764-583X
• Electronic ISSN: 1290-3841
• Publisher: EDP Sciences
• Peer Reviewed: Peer Reviewed
• Volume: 35
• Issue: 4
• Pages: 713-748
• DOI: https://doi.org/10.1051/m2an%3A2001133
• Keywords: Phase separation, Multi-component systems, Degenerate parabolic systems of fourth order, Finite element method, Convergence analysis.
• Public URL: https://durham-repository.worktribe.com/output/1599329
• Publisher URL: http://www.edpsciences.org/articles/m2an/abs/2001/04/m2an0034/m2an0034.html