带有随机输入的椭圆偏微分方程的混合有限元方法  

Mixed Finite Element Methods for Elliptic Partial Differential Equations with Random Data

作　　者：高蕾[1] 谢富纪[2] 

机构地区：[1]上海交通大学数学科学学院,上海200240 [2]上海交通大学安泰经济与管理学院,上海200030

出　　处：《上海交通大学学报》2016年第4期625-630,635,共7页Journal of Shanghai Jiaotong University

基　　金：国家自科学基金(11171216;71373158)资助

摘　　要：对具有齐次Dirichlet边界条件的线性随机椭圆型偏微分方程考虑了一类混合有限元方法,以同时高精度逼近未知函数与其扩散通量的统计矩.理论分析表明该方法对真解及其扩散通量的均值具有一阶最优逼近精度,数值实验也验证了理论结果的正确性.A class of mixed finite element methods for a linear elliptic problem with stochastic input data and homogeneous Dirichlet boundary conditions were considered to approximate statistical moments of the scalar function and its flux.Theoretical analysis shows that these methods have the first order optimal error estimates for the mean values of the stochastic solutions.Numerical experiments were developed to support the theoretical findings.

关 键 词：随机椭圆偏微分方程 混合有限元方法 最优误差估计 数值实验 

分 类 号：O241.82[理学—计算数学] O242.21[理学—数学]