各向异性、近似结晶、吉布斯-汤姆森定律的单侧Stefan问题的有限元逼近
Finite-Element Approximation of One-Sided Stefan Problems with Anisotropic, Approximately Crystalline, Gibbs--Thomson Law
摘要：
我们提出了一个有限元逼近的单侧Stefan问题和单侧Mullins-Sekerka问题，分别。问题的特点是完全各向异性吉布斯-汤姆逊定律，以及动力过冷。我们的近似，耦合参数近似的移动边界与有限元近似的批量，可以被证明是满足稳定的界限，它享有非常好的网格属性，这意味着没有网格平滑是必要的在实践中。在我们的数值计算中，我们集中在模拟雪晶的生长。在选择现实的物理参数，我们能够产生几种不同类型的雪晶形态。特别地，可以观察到近似结晶演变中的刻面断裂。
英文摘要：
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.
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