CSpace  > 计算数学与科学工程计算研究所
STRONG AND WEAK CONVERGENCE RATES OF A SPATIAL APPROXIMATION FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATION WITH ONE-SIDED LIPSCHITZ COEFFICIENT
Cui, Jianbo1,2; Hong, Jialin1,2
2019
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume57Issue:4Pages:1815-1841
AbstractStrong 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.
Keywordone-sided Lipschitz coefficient stochastic Allen-Cahn equation finite element method strong and weak convergence rate Kolmogorov equation Malliavin calculus
DOI10.1137/18M1215554
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000483942800012
PublisherSIAM PUBLICATIONS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35520
Collection计算数学与科学工程计算研究所
Corresponding AuthorCui, Jianbo
Affiliation1.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
Recommended Citation
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.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Cui, Jianbo]'s Articles
[Hong, Jialin]'s Articles
Baidu academic
Similar articles in Baidu academic
[Cui, Jianbo]'s Articles
[Hong, Jialin]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Cui, Jianbo]'s Articles
[Hong, Jialin]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.