Mullins-Sekerka问题的保结构前跟踪有限元方法

IF 3.8 2区数学 Q1 MATHEMATICS

Journal of Numerical Mathematics Pub Date : 2022-03-23 DOI:10.1515/jnma-2021-0131

R. Nürnberg

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引用次数: 4

摘要

摘要本文介绍并分析了比热可忽略的材料凝固和清算数学模型的完全离散近似。这个模型是一个双面Mullins-Sekerka问题。离散化采用空间有限元和运动自由边界的独立参数化。我们证明了所引入方案的无条件稳定性和精确体积守恒性。包括近晶体表面能在内的几个数值模拟表明了该数值方法的实用性和准确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A structure preserving front tracking finite element method for the Mullins–Sekerka problem

Abstract We introduce and analyse a fully discrete approximation for a mathematical model for the solidification and liquidation of materials of negligible specific heat. The model is a two-sided Mullins–Sekerka problem. The discretization uses finite elements in space and an independent parameterization of the moving free boundary. We prove unconditional stability and exact volume conservation for the introduced scheme. Several numerical simulations, including for nearly crystalline surface energies, demonstrate the practicality and accuracy of the presented numerical method.

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来源期刊

Journal of Numerical Mathematics 数学-数学

CiteScore

5.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.