A WEAK GALERKIN FINITE ELEMENT METHOD FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION-REACTION PROBLEMS

被引：109

作者：

Lin, Runchang ^{[1
]}

Ye, Xiu ^{[2
]}

Zhang, Shangyou ^{[3
]}

Zhu, Peng ^{[4
]}

机构：

[1] Texas A&M Int Univ, Dept Math & Phys, Laredo, TX 78041 USA

[2] Univ Arkansas, Dept Math, Little Rock, AR 72204 USA

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[4] Jiaxing Univ, Sch Math Phys & Informat, Jiaxing 314001, Zhejiang, Peoples R China

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2018年 / 56卷 / 03期

基金：

美国国家科学基金会;

关键词：

weak Galerkin; finite element method; discrete gradient; singular perturbation; convection-diffusion reaction; polyhedral mesh; 2ND-ORDER ELLIPTIC PROBLEMS; POLYTOPAL MESHES; EQUATIONS;

D O I：

10.1137/17M1152528

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, a new weak Galerkin finite element method is introduced to solve convection-diffusion-reaction equations in the convection dominated regime. Our method is highly flexible by allowing the use of discontinuous approximating functions on polytopal mesh without imposing extra conditions on the convection coefficient. An error estimate is devised in a suitable norm. Numerical examples are provided to confirm theoretical findings and efficiency of the method.

引用

页码：1482 / 1497

页数：16

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