陈明卿, 谢小平

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）.

WEAK GALERKIN FINITE ELEMENT METHODS FOR STOCHASTIC LINEAR PLANE ELASTICITY EQUATIONS

Chen Mingqing, Xie Xiaoping

School of Mathematics, Sichuan University, Chengdu 610064, China

Received:2019-12-17Online:2021-08-15Published:2021-08-20







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本文针对带有随机杨氏模量和荷载的平面线弹性问题，提出了一类随机弱Galerkin有限元方法.先利用Karhunen-Loève展开把随机项参数化，将方程转化为一个确定性问题；再采用弱Galerkin有限元法和$k$-/$p$-型方法分别离散空间区域和随机场.在弱Galerkin离散中，用分片$s（s\geqslant 1$）和$s+1$次多项式逼近单元内部的应力和位移，用分片$s$次多项式逼近位移在单元边界上的迹.证明了该方法关于空间网格尺度最优且与Lamé常数$\lambda$一致无关的误差估计.最后通过数值算例验证了理论结果.
MR(2010)主题分类:
65N12
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