随机平面线弹性问题的一类弱Galerkin方法  

WEAK GALERKIN FINITE ELEMENT METHODS FOR STOCHASTIC LINEAR PLANE ELASTICITY EQUATIONS

作　　者：陈明卿 谢小平[1] Chen Mingqing;Xie Xiaoping(School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《计算数学》2021年第3期279-300,共22页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11771312)。

摘　　要：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-Loeve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≥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Lame常数λ一致无关的误差估计.最后通过数值算例验证了理论结果.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-Loeve 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≥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 Lame constant λ.Finally,numerical experiments are performed to verify the theoretical results.

关 键 词：随机线弹性问题 K-L展开 WG有限元法 k-方法 p-方法 误差估计 

分 类 号：O241.82[理学—计算数学]