Uniform convergence of a weak Galerkin method for singularly perturbed convection-diffusion problems?

被引：6
|
作者：
Zhang, Jin [1 ]
Liu, Xiaowei [2 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China
[2] Qilu Univ Technol, Shandong Acad Sci, Sch Math & Stat, Jinan 250353, Peoples R China
来源：
MATHEMATICS AND COMPUTERS IN SIMULATION | 2022年 / 200卷
基金：
中国国家自然科学基金;
关键词：
Singular perturbation; Convection-diffusion equation; Bakhvalov-type mesh; Weak Galerkin method; FINITE-ELEMENT-METHOD; STABILIZATION; EQUATIONS;
D O I：
10.1016/j.matcom.2022.04.023
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this article, we analyze convergence of a weak Galerkin method on Bakhvalov-type mesh. This method uses piecewise polynomials of degree k >= 1 on the interior and piecewise constant on the boundary of each element. To obtain uniform convergence, we carefully define the penalty parameter and a new interpolant which is based on the characteristic of the Bakhvalov-type mesh. Then the method is proved to be convergent with optimal order, which is confirmed by numerical experiments. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：393 / 403
页数：11
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