• 论文 •

### 随机平面线弹性问题的一类弱Galerkin方法

1. 四川大学数学学院, 成都 610064
• 收稿日期:2019-12-17 出版日期:2021-08-15 发布日期:2021-08-20
• 通讯作者: 谢小平,Email:xpxie@scu.edu.cn.
• 基金资助:
国家自然科学基金（11771312）.

Chen Mingqing, Xie Xiaoping. WEAK GALERKIN FINITE ELEMENT METHODS FOR STOCHASTIC LINEAR PLANE ELASTICITY EQUATIONS[J]. Mathematica Numerica Sinica, 2021, 43(3): 279-300.

### WEAK GALERKIN FINITE ELEMENT METHODS FOR STOCHASTIC LINEAR PLANE ELASTICITY EQUATIONS

Chen Mingqing, Xie Xiaoping

1. School of Mathematics, Sichuan University, Chengdu 610064, China
• Received:2019-12-17 Online:2021-08-15 Published:2021-08-20

This paper proposes a class of stochastic weak Galerkin finite element methods for solving linear plane elasticity problems with stochastic Young's modulus and loads. Firstly, we convert the original system to a deterministic one by Karhuen-Loève expansion for Parameterizing the stochastic terms. Then we use a weak Galerkin (WG) discretization in the spatial domain and a $k$-/$p$- version method in the stochastic field. The WG method adopts piecewise-polynomial approximations of degrees $s(s\geqslant 1)$ and $s+1$ for the stress and displacement respectively, and $s$ for the displacement trace on the element boundaries. Optimal error estimates are derived which are uniform with respect to the Lamé constant $\lambda$. Finally, numerical experiments are performed to verify the theoretical results.

MR(2010)主题分类:

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