A splitting semi-implicit Euler method for stochastic incompressible Euler equations on T-2

doi:10.1093/imanum/drac054

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	A splitting semi-implicit Euler method for stochastic incompressible Euler equations on T-2
	Hong, Jialin ; Sheng, Derui ; Zhou, Tau 1
	2022-10-14
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
页码	29
摘要	The main difficulty in studying numerical methods for stochastic evolution equations (SEEs) lies in the treatment of the time discretization (Printems, 2001, ESAIM Math. Model. Numer. Anal. 35, 1055-1078). Although fruitful results on numerical approximations have been developed for SEEs, as far as we know, none of them include that of stochastic incompressible Euler equations. To bridge this gap, this paper proposes and analyzes a splitting semi-implicit Euler method in temporal direction for stochastic incompressible Euler equations on torus T-2 driven by additive noises. By a Galerkin approximation and the fixed-point technique, we establish the unique solvability of the proposed method. Based on the regularity estimates of both exact and numerical solutions, we measure the error in L-2(T-2) and show that the pathwise convergence order is nearly 1/2 and the convergence order in probability is almost 1.
关键词	stochastic incompressible Euler equation convergence order splitting semi-implicit Euler method
DOI	10.1093/imanum/drac054
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000868237500001
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/60741
专题	中国科学院数学与系统科学研究院
通讯作者	Zhou, Tau
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, 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	Hong, Jialin,Sheng, Derui,Zhou, Tau. A splitting semi-implicit Euler method for stochastic incompressible Euler equations on T-2[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2022:29.
APA	Hong, Jialin,Sheng, Derui,&Zhou, Tau.(2022).A splitting semi-implicit Euler method for stochastic incompressible Euler equations on T-2.IMA JOURNAL OF NUMERICAL ANALYSIS,29.
MLA	Hong, Jialin,et al."A splitting semi-implicit Euler method for stochastic incompressible Euler equations on T-2".IMA JOURNAL OF NUMERICAL ANALYSIS (2022):29.