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

被引：16

作者：

Barrett, John W. ^{[1
]}

Garcke, Harald ^{[2
]}

Nuernberg, Robert ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2013年 / 93卷 / 10-11期

关键词：

Phase field models; anisotropy; Allen-Cahn; Cahn-Hilliard; mean curvature flow; surface diffusion; Mullins-Sekerka; finite element approximation; FINITE-ELEMENT APPROXIMATION; CAHN-HILLIARD EQUATION; GEOMETRIC EVOLUTION-EQUATIONS; BOUNDARY MOTION; MEAN-CURVATURE; SHARP; SOLIDIFICATION; SURFACE; LIMIT; LAWS;

D O I：

10.1002/zamm.201200147

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：719 / 732

页数：14

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