KMS Of Academy of mathematics and systems sciences, CAS
| Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen-Cahn equation | |
Brehier, Charles-Edouard1; Cui, Jianbo2,3; Hong, Jialin2,3
| |
| 2019-10-01 | |
| Source Publication | IMA JOURNAL OF NUMERICAL ANALYSIS
 |
| ISSN | 0272-4979 |
| Volume | 39Issue:4Pages:2096-2134 |
| Abstract | This article analyses an explicit temporal splitting numerical scheme for the stochastic Allen-Cahn equation driven by additive noise in a bounded spatial domain with smooth boundary in dimension d <= 3. The splitting strategy is combined with an exponential Euler scheme of an auxiliary problem. When d = 1 and the driving noise is a space-time white noise we first show some a priori estimates of this splitting scheme. Using the monotonicity of the drift nonlinearity we then prove that under very mild assumptions on the initial data this scheme achieves the optimal strong convergence rate O(delta t(1/4)). When d <= 3 and the driving noise possesses some regularity in space we study exponential integrability properties of the exact and numerical solutions. Finally, in dimension d = 1, these properties are used to prove that the splitting scheme has a strong convergence rate O(delta t). |
| Keyword | stochastic Allen-Cahn equation splitting scheme strong convergence rate exponential integrability |
| DOI | 10.1093/imanum/dry052 |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000491253300017 |
| Publisher | OXFORD UNIV PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35890 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Cui, Jianbo |
| Affiliation | 1.Univ Claude Bernard Lyon 1, Univ Lyon, Inst Camille Jordan, CNRS,UMR 5208, F-69622 Villeurbanne, France 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Brehier, Charles-Edouard,Cui, Jianbo,Hong, Jialin. Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen-Cahn equation[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2019,39(4):2096-2134. |
| APA | Brehier, Charles-Edouard,Cui, Jianbo,&Hong, Jialin.(2019).Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen-Cahn equation.IMA JOURNAL OF NUMERICAL ANALYSIS,39(4),2096-2134. |
| MLA | Brehier, Charles-Edouard,et al."Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen-Cahn equation".IMA JOURNAL OF NUMERICAL ANALYSIS 39.4(2019):2096-2134. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment