On the stable discretization of strongly anisotropic phase field models with applications to crystal growth

We introduce unconditionally stable finite element approximations for anisotropic Allen–Cahn and Cahn–Hilliard equations. These equations frequently feature in phase field models that appear in materials science. On introducing the novel fully practical finite element approximations we prove their s...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Mechanik 2013-10, Vol.93 (10-11), p.719-732
Main Authors: Barrett, J.W., Garcke, H., Nürnberg, R.
Format: Article
Language:English
Subjects:
Allen-Cahn
Anisotropy
Approximation
Cahn-Hilliard
Crystal growth
Finite element analysis
finite element approximation
Finite element method
Materials science
Mathematical analysis
Mathematical models
mean curvature flow
Mullins-Sekerka
Phase field models
Stability
surface diffusion
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Summary:We introduce unconditionally stable finite element approximations for anisotropic Allen–Cahn and Cahn–Hilliard equations. These equations frequently feature in phase field models that appear in materials science. On introducing the novel fully practical finite element approximations we prove their stability and demonstrate their applicability with some numerical results. The authors introduce unconditionally stable finite element approximations for anisotropic Allen–Cahn and Cahn‐‐Hilliard equations. These equations frequently feature in phase field models that appear in materials science. On introducing the novel fully practical finite element approximations they prove their stability and demonstrate their applicability with some numerical results.
ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.201200147