Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2010) On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth. JOURNAL OF COMPUTATIONAL PHYSICS, 229 (18). pp. 6270-6299. ISSN 0021-9991, 1090-2716
Full text not available from this repository. (Request a copy)Abstract
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GEOMETRIC EVOLUTION-EQUATIONS; MEAN-CURVATURE FLOW; PHASE FIELD MODEL; NUMERICAL APPROXIMATION; MORPHOLOGICAL STABILITY; VOID ELECTROMIGRATION; PATTERN-FORMATION; SURFACE-TENSION; CRYSTAL-GROWTH; GRADIENT FLOWS; Stefan problem; Mullins-Sekerka problem; Surface tension; Anisotropy; Kinetic undercooling; Gibbs-Thomson law; Dendritic growth; Snow crystal growth; Parametric finite elements |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Jul 2020 05:51 |
| Last Modified: | 15 Jul 2020 05:51 |
| URI: | https://pred.uni-regensburg.de/id/eprint/24253 |
Actions (login required)
 |
View Item |
