Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen-Cahn equation
文献类型：期刊论文
| 作者 | Brehier, Charles-Edouard1; Cui, Jianbo2,3; Hong, Jialin2,3
|
| 刊名 | IMA JOURNAL OF NUMERICAL ANALYSIS
 |
| 出版日期 | 2019-10-01 |
| 卷号 | 39期号:4页码:2096-2134 |
| 关键词 | stochastic Allen-Cahn equation splitting scheme strong convergence rate exponential integrability |
| ISSN号 | 0272-4979 |
| DOI | 10.1093/imanum/dry052 |
| 英文摘要 | 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). |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000491253300017 |
| 出版者 | OXFORD UNIV PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/35889]  |
| 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.Univ Claude Bernard Lyon 1, Univ Lyon, Inst Camille Jordan, CNRS,UMR 5208, F-69622 Villeurbanne, France 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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