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Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs
Gong, Wei1; Hinze, Michael2; Zhou, Zhaojie3
2016-03-01
Source PublicationJOURNAL OF SCIENTIFIC COMPUTING
ISSN0885-7474
Volume66Issue:3Pages:941-967
AbstractFinite element approximations of Dirichlet boundary control problems governed by parabolic PDEs on convex polygonal domains are studied in this paper. The existence of a unique solution to optimal control problems is guaranteed based on very weak solution of the state equation and as control space. For the numerical discretization of the state equation we use standard piecewise linear and continuous finite elements for the space discretization of the state, while a dG(0) scheme is used for time discretization. The Dirichlet boundary control is realized through a space-time -projection. We consider both piecewise linear, continuous finite element approximation and variational discretization for the controls and derive a priori -error bounds for controls and states. We finally present numerical examples to support our theoretical findings.
KeywordOptimal control problem Parabolic equation Finite element method A priori error estimate Dirichlet boundary control
DOI10.1007/s10915-015-0051-2
Language英语
Funding ProjectAlexander von Humboldt Foundation ; National Basic Research Program of China[2012CB821204] ; National Natural Science Foundation of China[11201464] ; National Natural Science Foundation of China[91330115] ; National Natural Science Foundation of China[11301311] ; scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry ; DFG Priority Program 1253
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000369911500003
PublisherSPRINGER/PLENUM PUBLISHERS
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Cited Times:5[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/22009
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, LSEC, Beijing 100190, Peoples R China
2.Univ Hamburg, Schwerpunkt Optimierung & Approximat, Bundesstr 55, D-20146 Hamburg, Germany
3.Shandong Normal Univ, Sch Math Sci, Jinan 250014, Peoples R China
Recommended Citation
GB/T 7714
Gong, Wei,Hinze, Michael,Zhou, Zhaojie. Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs[J]. JOURNAL OF SCIENTIFIC COMPUTING,2016,66(3):941-967.
APA Gong, Wei,Hinze, Michael,&Zhou, Zhaojie.(2016).Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs.JOURNAL OF SCIENTIFIC COMPUTING,66(3),941-967.
MLA Gong, Wei,et al."Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs".JOURNAL OF SCIENTIFIC COMPUTING 66.3(2016):941-967.
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