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

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

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


Authors

J.W. Barrett

H. Garcke



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 Mar 29, 2024
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.
Publisher URL http://www.edpsciences.org/articles/m2an/abs/2001/04/m2an0034/m2an0034.html

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Copyright Statement
© EDP Sciences, SMAI 2001




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