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We present a finite-element approximation for the one-sided Stefan problemand the one-sided Mullins--Sekerka problem, respectively. The problems featurea fully anisotropic Gibbs--Thomson law, as well as kinetic undercooling. Ourapproximation, which couples a parametric approximation of the moving boundarywith a finite element approximation of the bulk quantities, can be shown tosatisfy a stability bound, and it enjoys very good mesh properties which meansthat no mesh smoothing is necessary in practice. In our numerical computationswe concentrate on the simulation of snow crystal growth. On choosing realisticphysical parameters, we are able to produce several distinctive types of snowcrystal morphologies. In particular, facet breaking in approximatelycrystalline evolutions can be observed.

Finite-Element Approximation of One-Sided Stefan Problems with Anisotropic, Approximately Crystalline, Gibbs--Thomson Law