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：

俄罗斯基础研究基金会; 中国国家自然科学基金;

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.

引用

页码：732 / 758

页数：27

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