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.
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页码：906 / 916
页数：11
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