• 青年评述 •

### 弱有限元方法在线弹性问题中的应用

1. 吉林大学数学学院, 长春 130012
• 收稿日期:2020-01-04 出版日期:2020-02-15 发布日期:2020-02-15
• 作者简介:张然,吉林大学数学学院教授.1999年和2004年在吉林大学分别获得学士和博士学位,2008年任吉林大学教授.主要研究领域包括有限元方法、随机微分、积分方程数值解、多尺度分析及应用.曾入选教育部新世纪人才奖励计划(2013)、入选教育部"长江学者奖励计划"青年学者(2016)等.截止目前,在学术期刊上发表论文60余篇.
• 基金资助:

国家自然科学基金（11971198、11726102、11771179）和中国教育部长江学者计划以及吉林大学符号计算与知识工程教育部重点实验室等资助

Zhang Ran. WEAK GALERKIN FINITE ELEMENT METHOD FOR LINEAR ELASTICITY PROBLEMS[J]. Mathematica Numerica Sinica, 2020, 42(1): 1-17.

### WEAK GALERKIN FINITE ELEMENT METHOD FOR LINEAR ELASTICITY PROBLEMS

Zhang Ran

1. School of Mathematics, Jilin University, ChangChun 130012, China
• Received:2020-01-04 Online:2020-02-15 Published:2020-02-15

This article considers the application of the weak Galerkin finite element (WG) method to linear elasticity problems. The WG method is a generalization of the traditional finite element method, which is used to solve numerical solutions of partial differential equations. In WG, the weak function, a piecewise polynomial function that is defined both inside the element and on the boundary of the element, is used as an approximate function and weak differential operators are given correspondingly. Moreover, stabilizers are introduced to keep the weak continuity of the approximate function. In the WG method, partitions could be arbitrary polygons or polyhedrons that satisfies the shape regular conditions. In addition the numerical format and the approximate function are easy to construct. In this paper, we introduce the application of the WG method in solving linear elasticity problems by solving three common problems in the numerical methods for linear elasticity problems, namely: the coerciveness, locking property, and the symmetry of stress tensor.

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