STRONG AND WEAK CONVERGENCE RATES OF A SPATIAL APPROXIMATION FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATION WITH ONE-SIDED LIPSCHITZ COEFFICIENT

doi:10.1137/18M1215554

	STRONG AND WEAK CONVERGENCE RATES OF A SPATIAL APPROXIMATION FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATION WITH ONE-SIDED LIPSCHITZ COEFFICIENT
	Cui, Jianbo 1,2; Hong, Jialin1,2
	2019
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	57 期号:4 页码:1815-1841
摘要	Strong and weak approximation errors of a spatial finite element method are analyzed for the stochastic partial differential equations (SPDEs) with one-sided Lipschitz coefficients, including the stochastic Allen-Cahn equation, driven by additive noise. In order to give the strong convergence rate of the finite element method, we present an appropriate decomposition and some a priori estimates of the discrete stochastic convolution. To the best of our knowledge, there have been no essentially sharp weak convergence rates of spatial approximations for parabolic SPDEs with non-globally Lipschitz coefficients. To investigate the weak error, we first regularize the original equation by the splitting technique and obtain the regularity estimate the corresponding regularized Kolmogorov equation. Meanwhile, we present the refined estimates and the regularity estimate in the Malliavin sense of the finite element methods. Combining with the regularity of regularized Kolmogorov equation and Malliavin integration by parts, the weak convergence rate is shown to be twice the strong convergence rate.
关键词	one-sided Lipschitz coefficient stochastic Allen-Cahn equation finite element method strong and weak convergence rate Kolmogorov equation Malliavin calculus
DOI	10.1137/18M1215554
语种	英语
资助项目	National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[11290142]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000483942800012
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35520
专题	计算数学与科学工程计算研究所
通讯作者	Cui, Jianbo
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Cui, Jianbo,Hong, Jialin. STRONG AND WEAK CONVERGENCE RATES OF A SPATIAL APPROXIMATION FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATION WITH ONE-SIDED LIPSCHITZ COEFFICIENT[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2019,57(4):1815-1841.
APA	Cui, Jianbo,&Hong, Jialin.(2019).STRONG AND WEAK CONVERGENCE RATES OF A SPATIAL APPROXIMATION FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATION WITH ONE-SIDED LIPSCHITZ COEFFICIENT.SIAM JOURNAL ON NUMERICAL ANALYSIS,57(4),1815-1841.
MLA	Cui, Jianbo,et al."STRONG AND WEAK CONVERGENCE RATES OF A SPATIAL APPROXIMATION FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATION WITH ONE-SIDED LIPSCHITZ COEFFICIENT".SIAM JOURNAL ON NUMERICAL ANALYSIS 57.4(2019):1815-1841.