On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Barrett, John W.¹  Garcke, Harald²  Nuernberg, Robert¹ 

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

[2] Univ Regensburg, NWF 1, D-93040 Regensburg, Germany

关键词: Stefan problem;    Mullins-Sekerka problem;    Surface tension;    Anisotropy;    Kinetic undercooling;    Gibbs-Thomson law;    Dendritic growth;    Snow crystal growth;    Parametric finite elements;   

DOI  :  10.1016/j.jcp.2010.04.039

来源: Elsevier

【 摘 要 】

We introduce a parametric finite element approximation for the Stefan problem with the Gibbs-Thomson law and kinetic undercooling, which mimics the underlying energy structure of the problem. The proposed method is also applicable to certain quasi-stationary variants, such as the Mullins-Sekerka problem. In addition, fully anisotropic energies are easily handled. The approximation has good mesh properties, leading to a well-conditioned discretization, even in three space dimensions. Several numerical computations, including for dendritic growth and for snow crystal growth, are presented. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free