Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen-Cahn equation

doi:10.1093/imanum/dry052

	Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen-Cahn equation
	Brehier, Charles-Edouard 1; Cui, Jianbo 2,3; Hong, Jialin2,3
	2019-10-01
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	39 期号:4 页码:2096-2134
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).
关键词	stochastic Allen-Cahn equation splitting scheme strong convergence rate exponential integrability
DOI	10.1093/imanum/dry052
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:000491253300017
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35890
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.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
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.