Translator Disclaimer
March/April 2013 Finite Element Approximation of One-Sided Stefan Problems with Anisotropic, Approximately Crystalline, Gibbs--Thomson Law
John W. Barrett, Harald Garcke, Robert Nürnberg
Adv. Differential Equations 18(3/4): 383-432 (March/April 2013).

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.

Citation

Download Citation

John W. Barrett. Harald Garcke. Robert Nürnberg. "Finite Element Approximation of One-Sided Stefan Problems with Anisotropic, Approximately Crystalline, Gibbs--Thomson Law." Adv. Differential Equations 18 (3/4) 383 - 432, March/April 2013.

Information

Published: March/April 2013
First available in Project Euclid: 5 February 2013

zbMATH: 1271.80005
MathSciNet: MR3060200

Subjects:
Primary: 35R37 , 65M12 , 65M60 , 74N05 , 80A22 , 80M10

Rights: Copyright © 2013 Khayyam Publishing, Inc.

JOURNAL ARTICLE
50 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.18 • No. 3/4 • March/April 2013
Back to Top