A stabilized finite element method for advection-diffusion equations on surfaces
A stabilized finite element method for advection-diffusion equations on surfaces
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DOI：
10.1093/imanum/drt016
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发表时间：
2014-04-01
影响因子：
2.1
通讯作者：
Xu, Xianmin
中科院分区：
文献类型：
--
作者：
Olshanskii, Maxim A.;Reusken, Arnold;Xu, Xianmin
应用最近发展起来的欧拉有限元方法来求解超曲面上的对流扩散方程。当表面上的传输过程超过扩散时，除非网格足够细，否则FEMS往往是不稳定的。本文介绍了一种基于流线迎风Petrov-Galerkin(SUPG)技术的稳定有限元格式。给出了该方法的误差分析。最后给出了数值实验结果，验证了稳定化方法的有效性。
A recently developed Eulerian finite element method (FEM) is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, FEMs tend to be unstable unless the mesh is sufficiently fine. The paper introduces a stabilized FE formulation based on the streamline upwind Petrov-Galerkin (SUPG) technique. An error analysis of the method is given. Results of numerical experiments are presented, which illustrate the performance of the stabilized method.