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

doi:10.1093/imanum/drac054

	A splitting semi-implicit Euler method for stochastic incompressible Euler equations on T-2
	Hong, Jialin ; Sheng, Derui ; Zhou, Tau 1
刊名	IMA JOURNAL OF NUMERICAL ANALYSIS
	2022-10-14
页码	29
关键词	stochastic incompressible Euler equation convergence order splitting semi-implicit Euler method
ISSN号	0272-4979
DOI	10.1093/imanum/drac054
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	OXFORD UNIV PRESS
WOS记录号	WOS:000868237500001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60740]
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.