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A BALANCED OVERSAMPLING FINITE ELEMENT METHOD FOR ELLIPTIC PROBLEMS WITH OBSERVATIONAL BOUNDARY DATA
Chen, Zhiming1,2; Tuo, Rui3,4; Zhang, Wenlong2,5
2020
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume38Issue:2Pages:355-374
AbstractIn 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.
KeywordObservational boundary data Elliptic equation Sub-Gaussian random variable
DOI10.4208/jcm.1810-m2017-0168
Indexed BySCI
Language英语
Funding ProjectNational Center for Mathematics and Interdisciplinary Sciences, CAS ; China NSF[118311061] ; China NSF[11501551]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000514843500006
PublisherGLOBAL SCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50905
Collection中国科学院数学与系统科学研究院
Corresponding AuthorChen, Zhiming
Affiliation1.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
Recommended Citation
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.
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