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

doi:10.4208/jcm.1810-m2017-0168

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	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
	2020
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	38 期号:2 页码:355-374
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.
关键词	Observational boundary data Elliptic equation Sub-Gaussian random variable
DOI	10.4208/jcm.1810-m2017-0168
收录类别	SCI
语种	英语
资助项目	National Center for Mathematics and Interdisciplinary Sciences, CAS ; China NSF[118311061] ; China NSF[11501551]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000514843500006
出版者	GLOBAL SCIENCE 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/50905
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.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China 4.Texas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USA 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.