John W. Barrett
Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System
Barrett, John W.; Blowey, James F.
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 |
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