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 ...
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.
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