A stabilized finite element method for advection-diffusion equations on surfaces

被引：54
|
作者：
Olshanskii, Maxim A. [1 ,2 ]
Reusken, Arnold [3 ]
Xu, Xianmin [4 ]
机构：
[1] Univ Houston, Dept Math, Houston, TX 77204 USA
[2] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow 119899, Russia
[3] Rhein Westfal TH Aachen, Inst Geometrie & Prakt Math, D-52056 Aachen, Germany
[4] Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, LSEC, NCMIS,AMSS, Beijing 100190, Peoples R China
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2014年 / 34卷 / 02期
基金：
中国国家自然科学基金; 俄罗斯基础研究基金会;
关键词：
surface PDE; finite element method; transport equations; advection-diffusion equation; SUPG stabilization;
D O I：
10.1093/imanum/drt016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：732 / 758
页数：27
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