A locking-free weak Galerkin finite element method for Reissner-Mindlin plate on polygonal meshes

被引：13

作者：

Ye, Xiu ^{[1
]}

Zhang, Shangyou ^{[2
]}

Zhang, Zhimin ^{[3
,4
]}

机构：

[1] Univ Arkansas, Dept Math, Little Rock, AR 72204 USA

[2] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

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

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

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2020年 / 80卷 / 05期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Weak Galerkin; Finite element methods; Discrete gradient; The Reissner-Mindlin plate; Polygonal meshes; DISCONTINUOUS GALERKIN; APPROXIMATION; CONVERGENCE;

D O I：

10.1016/j.camwa.2020.05.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new weak Galerkin finite element method is introduced and analyzed for the Reissner-Mindlin plate model in the primary form (without introducing shear strain as an extra unknown), which results in a linear system with symmetric positive definite stiffness matrix. The proposed method achieves uniform convergence with respect to plate thickness (the so-called locking-free) without introducing any projection, reduced integration, etc. In addition, the new method can be applied to general polygonal meshes; in particular, we implement pentagonal and hexagonal meshes in our numerical tests. The numerical study confirms our theory. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页码：906 / 916

页数：11

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