A-posteriori error estimation in maximum norm for a strongly coupled system of two singularly perturbed convection-diffusion problems

被引：17

作者：

Liu, Li-Bin ^{[1
]}

Chen, Yanping ^{[2
]}

机构：

[1] Guangxi Teachers Educ Univ, Coll Math & Stat, Nanning 530001, Peoples R China

[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2017年 / 313卷

基金：

美国国家科学基金会;

关键词：

Singularly perturbed; Strongly coupled; Convection-diffusion; Maximum norm; UNIFORM POINTWISE CONVERGENCE; BOUNDARY-VALUE-PROBLEMS; EQUATIONS; MESHES;

D O I：

10.1016/j.cam.2016.08.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A system of two singularly perturbed convection-diffusion problems with strong coupling is studied. This system is discretized by an upwind finite difference scheme on an arbitrary non-uniform mesh. An a posteriori error estimation in the maximum norm is derived. Based on the a posteriori error estimation, a monitor function is proposed to design an adaptive grid algorithm. Especially, to implement the adaptive grid approach, we not only give a mesh generation algorithm, but also give a sub-algorithm, which is called an arc-length equidistribution algorithm. Numerical results are given to confirm our theoretical result. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：152 / 167

页数：16

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