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.
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页码：152 / 167
页数：16
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