On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth

Barrett J.W.; Garcke H.; Nürnberg Robert R.

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On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth

机译：Stefan问题和Mullins-Sekerka问题的稳定参数有限元方法及其在树突生长中的应用

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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.

机译：我们使用吉布斯-汤姆森定律和动力学过冷为Stefan问题引入了参数有限元逼近，它模仿了问题的潜在能量结构。所提出的方法还适用于某些准平稳变体，例如Mullins-Sekerka问题。另外，完全各向异性的能量易于处理。该近似具有良好的网格特性，即使在三个空间维度上，也导致条件良好的离散化。提出了几种数值计算方法，包括树突生长和雪晶生长的数值计算。

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《Journal of Computational Physics》 |2010年第18期|共30页
作者
Barrett J.W.; Garcke H.; Nürnberg Robert R.;
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正文语种 eng
中图分类数学物理方法;
关键词
Anisotropy; Dendritic growth; Gibbs-Thomson law; Kinetic undercooling; Mullins-Sekerka problem; Parametric finite elements; Snow crystal growth; Stefan problem; Surface tension;

机译：各向异性;树枝状生长;吉布斯-汤姆森定律;运动过冷;Mullins-Sekerka问题;参数有限元;雪晶生长;Stefan问题;表面张力;

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专利

1. On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth [J] . Barrett J.W., Garcke H., Nürnberg Robert R. Journal of Computational Physics . 2010,第18期

机译：Stefan问题和Mullins-Sekerka问题的稳定参数有限元方法及其在树突生长中的应用
2. A practical method for computation of ductile crack growth by means of finite elements and parametric 3D-modelling [J] . F. Baumjohann, J. Kroning Nuclear Engineering and Design . 1999,第1a2期

机译：有限元和参数3D建模计算延性裂纹扩展的实用方法
3. Efficient computation of dendritic growth with r-adaptive finite element methods [J] . Wang H, Li R, Tang T Journal of Computational Physics . 2008,第12期

机译：r自适应有限元方法有效计算树突生长
4. Research the Effect of Forced Flow on Dendritic Growth with Adaptive Finite Element Method [C] . Changsheng Zhu, Peng Lei, Rongzhen Xiao International Conference on Materials Science and Computational Engineering . 2014

机译：采用自适应有限元法研究强制流动对树枝状生长的影响
5. Extended finite element and level set methods with applications to growth of cracks and biofilms. [D] . Bordas, Stephane. 2003

机译：扩展的有限元和水平集方法，应用于裂缝和生物膜的生长。
6. Parametric Design Optimisation of Proximal Humerus Plates Based on Finite Element Method [O] . Ali Jabran, Chris Peach, Zhenmin Zou, -1

机译：基于有限元方法的肱骨近端板参数化设计优化
7. On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth [O] . Barrett John W., Garcke Harald, Nürnberg Robert 2010

机译：Stefan问题和Mullins-Sekerka问题的稳定参数有限元方法及其在树突生长中的应用
8. Application of the Finite-Element Method to Heat-Transfer Problems. Part I. Finite-Element Method Applied to Heat-Conduction Solids with Nonlinear Boundary Conditions [R] . Chu, S. C., Yalamanchili, R. V. S. 1971

机译：有限元法在传热问题中的应用。第一部分有限元法在非线性边界条件下的导热固体中的应用

On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth

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