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Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System

Barrett, John W.; Blowey, James F.

Authors

John W. Barrett



Abstract

We consider a fully practical finite element approximation of an Allen--Cahn/Cahn--Hilliard system with a degenerate mobility and a logarithmic free energy. This system arises in the modeling of phase separation and ordering in binary alloys. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Finally, some numerical experiments are presented.

Citation

Barrett, J. W., & Blowey, J. F. (2001). Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System. SIAM Journal on Numerical Analysis, 39(5), 1598-1624. https://doi.org/10.1137/s0036142900382144

Journal Article Type Article
Publication Date 2001
Journal SIAM Journal on Numerical Analysis
Print ISSN 0036-1429
Electronic ISSN 1095-7170
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 39
Issue 5
Pages 1598-1624
DOI https://doi.org/10.1137/s0036142900382144
Keywords Degenerate second/fourth order parabolic equations, Degenerate parabolic system, Allen--Cahn/Cahn--Hilliard, Order-disorder, Phase separation, Finite elements, Convergence analysis.
Public URL https://durham-repository.worktribe.com/output/1629414