FULL-DISCRETE FINITE ELEMENT METHOD FOR STOCHASTIC HYPERBOLIC EQUATION

作     者：Xiaoyuan Yang Xiaocui Li Ruisheng Qi Yinghan Zhang 

作者机构：Department of Mathematics Beihang UniversityLMIB of the Ministry of Education Beijing 100191 China Department of Mathematics Northeastern University at Qinhuangdao China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2015年第33卷第5期

页      面：533-556页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：The authors would like to express their sincere gratitude to the anony- mous reviewers for their careful reading of the manuscript  as well as their comments that lead to a considerable improvement of the original manuscript. The first author was supported by the National Natural Science Foundation of China under grant 61271010 and by Beijing Natural Science Foundation under grant 4152029 

主　　题：Stochastic hyperbolic equation Strong convergence Additive noise Wiener process. 

摘      要：This paper is concerned with the finite element method for the stochastic wave equation and the stochastic elastic equation driven by space-time white noise. For simplicity~ we rewrite the two types of stochastic hyperbolic equations into a unified form. We convert the stochastic hyperbolic equation into a regularized equation by discretizing the white noise and then consider the full-discrete finite element method for the regularized equation. We derive the modeling error by using “Green＇s method and the finite element approximation error by using the error estimates of the deterministic equation. Some numerical examples are presented to verify the theoretical results.