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Adaptive finite element method for elliptic optimal control problems: convergence and optimality
Gong, Wei1; Yan, Ningning2
2017-04-01
Source PublicationNUMERISCHE MATHEMATIK
ISSN0029-599X
Volume135Issue:4Pages:1121-1170
AbstractIn this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and piecewise linear and continuous finite elements to approximate the state variable. Based on the well-established convergence theory of AFEM for elliptic boundary value problems, we rigorously prove the convergence and quasi-optimality of AFEM for optimal control problems with respect to the state and adjoint state variables, by using the so-called perturbation argument. Numerical experiments confirm our theoretical analysis.
DOI10.1007/s00211-016-0827-9
Language英语
Funding ProjectNational Basic Research Program of China[2012CB821204] ; National Natural Science Foundation of China[11201464] ; National Natural Science Foundation of China[91530204] ; National Natural Science Foundation of China[11171337]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000398175500006
PublisherSPRINGER HEIDELBERG
Citation statistics
Cited Times:7[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25195
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, NCMIS,LSEC, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Gong, Wei,Yan, Ningning. Adaptive finite element method for elliptic optimal control problems: convergence and optimality[J]. NUMERISCHE MATHEMATIK,2017,135(4):1121-1170.
APA Gong, Wei,&Yan, Ningning.(2017).Adaptive finite element method for elliptic optimal control problems: convergence and optimality.NUMERISCHE MATHEMATIK,135(4),1121-1170.
MLA Gong, Wei,et al."Adaptive finite element method for elliptic optimal control problems: convergence and optimality".NUMERISCHE MATHEMATIK 135.4(2017):1121-1170.
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