带有随机输入的椭圆偏微分方程的混合有限元方法

上海交通大学学报（自然版） ›› 2016, Vol. 50 ›› Issue (04): 625-630.

带有随机输入的椭圆偏微分方程的混合有限元方法

高蕾a，谢富纪b

（上海交通大学 a.数学科学学院，上海 200240； b.安泰经济与管理学院，上海 200030）

收稿日期:2015-04-11 出版日期:2016-04-28 发布日期:2016-04-28
基金资助:
国家自科学基金(11171216;71373158)资助

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

GAO Leia，XIE Fujib

(a. School of Mathematical Sciences, Shanghai 200240； b. Anti College of Economics and Mangagement, Shanghai Jiaotong University, Shanghai 200030, China)

Received:2015-04-11 Online:2016-04-28 Published:2016-04-28

摘要/Abstract

摘要： 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.

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

Abstract: Abstract： 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.

Key words: Key words： stochastic elliptic partial differential equations, mixed finite element methods, optimal order error estimates, numerical experients

中图分类号:

高蕾a，谢富纪b. 带有随机输入的椭圆偏微分方程的混合有限元方法[J]. 上海交通大学学报（自然版）, 2016, 50(04): 625-630.

GAO Leia，XIE Fujib. Mixed Finite Element Methods for Elliptic Partial Differential Equations with Random Data[J]. Journal of Shanghai Jiaotong University, 2016, 50(04): 625-630.

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