Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility,

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

Abstract

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.

Citation

Blowey, J., & Barrett, J. (1999). Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility,. Mathematics of Computation, 68(226), 487-517. https://doi.org/10.1090/s0025-5718-99-01015-7

• Journal Article Type: Article
• Publication Date: 1999
• Journal: Mathematics of Computation
• Print ISSN: 0025-5718
• Electronic ISSN: 1088-6842
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 68
• Issue: 226
• Pages: 487-517
• DOI: https://doi.org/10.1090/s0025-5718-99-01015-7
• Public URL: https://durham-repository.worktribe.com/output/1623120