An ALE ESFEM for Solving PDEs on Evolving Surfaces
An ALE ESFEM for Solving PDEs on Evolving Surfaces
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DOI：
10.1007/s00032-012-0195-6
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发表时间：
2012-11
影响因子：
1.7
通讯作者：
C. M. Elliott;V. Styles
中科院分区：
文献类型：
--
作者：
C. M. Elliott;V. Styles
提出了用演化三角化曲面上的曲面有限元逼近演化超曲面上偏微分方程的数值方法。在ALE ESFEM中，三角形的顶点以垂直于超曲面的速度演化，同时具有任意的切向速度。这是在原来的不断发展的表面有限元方法，其中的节点与材料的速度移动。数值实验表明，选择任意切向速度对提高网格质量是有价值的。在材料科学和生物学中出现的两个应用程序的模拟耦合的表面的演化的表面偏微分方程的解决方案。
Numerical methods for approximating the solution of partial differential equations on evolving hypersurfaces using surface finite elements on evolving triangulated surfaces are presented. In the ALE ESFEM the vertices of the triangles evolve with a velocity which is normal to the hypersurface whilst having a tangential velocity which is arbitrary. This is in contrast to the original evolving surface finite element method in which the nodes move with a material velocity. Numerical experiments are presented which illustrate the value of choosing the arbitrary tangential velocity to improve mesh quality. Simulations of two applications arising in material science and biology are presented which couple the evolution of the surface to the solution of the surface partial differential equation.