Crouzeix-Raviart and Raviart-Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition

被引：4

作者：

Ishizaka, Hiroki ^{[1
]}

Kobayashi, Kenta ^{[2
]}

Tsuchiya, Takuya ^{[1
]}

机构：

[1] Ehime Univ, Grad Sch Sci & Engn, Matsuyama, Ehime, Japan

[2] Hitotsubashi Univ, Grad Sch Business Adm, Kunitachi, Tokyo, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2021年 / 38卷 / 02期

关键词：

Finite element; Raviart– Thomas; Crouzeix– Raviart; Anisotropic meshes;

D O I：

10.1007/s13160-020-00455-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the piecewise linear nonconforming Crouzeix-Raviart and the lowest order Raviart-Thomas finite-element methods for the Poisson problem on three-dimensional anisotropic meshes. We first give error estimates of the Crouzeix-Raviart and the Raviart-Thomas finite-element approximate problems. We next present the equivalence between the Raviart-Thomas finite-element method and the enriched Crouzeix-Raviart finite-element method. We emphasize that we do not impose either shape-regular or maximum-angle condition during mesh partitioning. Numerical results confirm the results that we obtained.

引用

页码：645 / 675

页数：31

共 34 条

[1] Crouzeix–Raviart and Raviart–Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition
Hiroki Ishizaka
Kenta Kobayashi
Takuya Tsuchiya
[J]. Japan Journal of Industrial and Applied Mathematics, 2021, 38 : 645 - 675
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Kobayashi, Kenta
Tsuchiya, Takuya
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