Convergence of a finite element method on a Bakhvalov-type mesh for singularly perturbed reaction-diffusion equation

被引：9

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：

APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 385卷

基金：

中国国家自然科学基金;

关键词：

Singular perturbation; Reaction-diffusion equation; Bakhvalov-type mesh; Finite element method; Higher-order; Uniform convergence; BOUNDARY-VALUE-PROBLEMS; SHISHKIN MESH;

D O I：

10.1016/j.amc.2020.125403

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A finite element method is applied on a Bakhvalov-type mesh to solve a singularly perturbed reaction-diffusion problem whose solution exhibits boundary layers. A uniform convergence order of O(N-(k+1) + epsilon(1/2N-k)) is proved, where k is the order of piecewise polynomials in the finite element method, eis the diffusion parameter and N is the number of partitions in each direction. Numerical experiments support this theoretical result. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：9

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