Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2013) FINITE-ELEMENT APPROXIMATION OF ONE-SIDED STEFAN PROBLEMS WITH ANISOTROPIC, APPROXIMATELY CRYSTALLINE, GIBBS-THOMSON LAW. ADVANCES IN DIFFERENTIAL EQUATIONS, 18 (3-4). pp. 383-432. ISSN 1079-9389,
Full text not available from this repository.Abstract
We present a finite-element approximation for the one-sided Stefan problem and the one-sided Mullins-Sekerka problem, respectively. The problems feature a fully anisotropic Gibbs-Thomson law, as well as kinetic undercooling. Our approximation, which couples a parametric approximation of the moving boundary with a finite-element approximation of the bulk quantities, can be shown to satisfy a stability bound, and it enjoys very good mesh properties, which means that no mesh smoothing is necessary in practice. In our numerical computations we concentrate on the simulation of snow crystal growth. On choosing realistic physical parameters, we are able to produce several distinctive types of snow crystal morphologies. In particular, facet breaking in approximately crystalline evolutions can be observed.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GEOMETRIC EVOLUTION-EQUATIONS; PHASE FIELD MODEL; VOID ELECTROMIGRATION; SNOW CRYSTALS; GROWTH; VAPOR; COMPUTATION; STABILITY; ALGORITHM; SURFACES; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 24 Apr 2020 05:51 |
| Last Modified: | 24 Apr 2020 05:51 |
| URI: | https://pred.uni-regensburg.de/id/eprint/17100 |
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