ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 67, 1 (1998)
pp. 57-68

APPROXIMATION OF CRYSTALLINE DENDRITE GROWTH IN TWO SPACE DIMENSIONS
A. SCHMIDT

Abstract. The phase transition between solid and liquid in an undercooled liquid leads to dendritic growth of the solid phase. The problem is modelled by the Stefan problem with a modified Gibbs-Thomson law, which includes the anisotropic mean curvature corresponding to a surface energy that depends on the direction of the interface normal. A finite element method for discretization of the Stefan problem is described which is based on a weak formulation of the anisotropic mean curvature flow. Numerical experiments with a nearly crystalline anisotropy are presented.

AMS subject classification. 65C20, 65N30, 65N50, 80A22, 80-08, 35K55, 35R35
Keywords.

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Acta Mathematica Universitatis Comenianae
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Comenius University
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