Supercloseness in a balanced norm of finite element methods on Shishkin and Bakhvalov-Shishkin rectangular meshes for reaction-diffusion problems

被引：4
|
作者：
Zhang, Jin [1 ]
Liu, Xiaowei [2 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan, Peoples R China
[2] Qilu Univ Technol, Shandong Acad Sci, Sch Math & Stat, Jinan 250353, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2022年 / 45卷 / 04期
基金：
中国国家自然科学基金;
关键词：
balanced norm; Bakhvalov-Shishkin mesh; finite element method; reaction-diffusion equation; Shishkin mesh; singular perturbation; supercloseness; BOUNDARY-VALUE-PROBLEMS; HYBRID NANOFLUID; SDFEM; CONVERGENCE; STABILITY; EQUATION;
D O I：
10.1002/mma.7920
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a convergence analysis for finite element methods of any order, which are applied on Shishkin mesh and Bakhvalov-Shishkin mesh to a singularly perturbed reaction-diffusion problem. A new interpolant is introduced for analysis in the balanced norm. By means of this interpolant and some superconvergence estimations, we prove supercloseness results in the cases of Shishkin mesh and Bakhvalov-Shishkin mesh. Numerical experiments also support these theoretical results.
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页码：2204 / 2218
页数：15
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