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.
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页数：9
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