A BALANCED OVERSAMPLING FINITE ELEMENT METHOD FOR ELLIPTIC PROBLEMS WITH OBSERVATIONAL BOUNDARY DATA

doi:10.4208/jcm.1810-m2017-0168

	A BALANCED OVERSAMPLING FINITE ELEMENT METHOD FOR ELLIPTIC PROBLEMS WITH OBSERVATIONAL BOUNDARY DATA
	Chen, Zhiming 1,2; Tuo, Rui 3,4; Zhang, Wenlong 2,5
刊名	JOURNAL OF COMPUTATIONAL MATHEMATICS
	2020
卷号	38 期号:2 页码:355-374
关键词	Observational boundary data Elliptic equation Sub-Gaussian random variable
ISSN号	0254-9409
DOI	10.4208/jcm.1810-m2017-0168
英文摘要	In this paper we propose a finite element method for solving elliptic equations with observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier and requires balanced oversampling of the measurements of the boundary data to control the random noises. We show the convergence of the random finite element error in expectation and, when the noise is sub-Gaussian, in the Orlicz psi(2)-norm which implies the probability that the finite element error estimates are violated decays exponentially. Numerical examples are included.
资助项目	National Center for Mathematics and Interdisciplinary Sciences, CAS ; China NSF[118311061] ; China NSF[11501551]
WOS研究方向	Mathematics
语种	英语
出版者	GLOBAL SCIENCE PRESS
WOS记录号	WOS:000514843500006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50904]
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Zhiming
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Texas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USA 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China 5.Southern Univ Sci & Technol, Shenzhen 518055, Peoples R China
推荐引用方式 GB/T 7714	Chen, Zhiming,Tuo, Rui,Zhang, Wenlong. A BALANCED OVERSAMPLING FINITE ELEMENT METHOD FOR ELLIPTIC PROBLEMS WITH OBSERVATIONAL BOUNDARY DATA[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2020,38(2):355-374.
APA	Chen, Zhiming,Tuo, Rui,&Zhang, Wenlong.(2020).A BALANCED OVERSAMPLING FINITE ELEMENT METHOD FOR ELLIPTIC PROBLEMS WITH OBSERVATIONAL BOUNDARY DATA.JOURNAL OF COMPUTATIONAL MATHEMATICS,38(2),355-374.
MLA	Chen, Zhiming,et al."A BALANCED OVERSAMPLING FINITE ELEMENT METHOD FOR ELLIPTIC PROBLEMS WITH OBSERVATIONAL BOUNDARY DATA".JOURNAL OF COMPUTATIONAL MATHEMATICS 38.2(2020):355-374.