Local ultraconvergence of linear and bilinear finite element method for second order elliptic problems

被引：2

作者：

He, Wen-ming ^{[1
]}

Lin, Runchang ^{[2
]}

Zhang, Zhimin ^{[3
,4
]}

机构：

[1] Lingnan Normal Univ, Dept Math, Zhanjiang 524000, Guangdong, Peoples R China

[2] Texas A&M Int Univ, Dept Math & Phys, Laredo, TX 78041 USA

[3] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China

[4] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2020年 / 372卷 / 372期

基金：

中国国家自然科学基金;

关键词：

Ultraconvergence; Finite element; Interpolation; Richardson extrapolation; Local symmetry theory; Green function; RICHARDSON EXTRAPOLATION; PATCH RECOVERY; SUPERCONVERGENCE; MESHES; ERROR;

D O I：

10.1016/j.cam.2020.112715

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, local ultraconvergence in gradient of the bilinear and linear finite element solutions to two-dimensional second order elliptic problems has been investigated. Special interpolation postprocessing algorithms of numerical solutions by Richardson extrapolation have been developed. The local symmetry theory and estimates of discrete Green functions are used in the analysis. Numerical experiments are provided to confirm the theoretical findings. Published by Elsevier B.V.

引用

页数：19

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