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Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs

文献类型：期刊论文

作者Gong, Wei1; Hinze, Michael2; Zhou, Zhaojie3
刊名JOURNAL OF SCIENTIFIC COMPUTING
出版日期2016-03-01
卷号66期号:3页码:941-967
关键词Optimal control problem Parabolic equation Finite element method A priori error estimate Dirichlet boundary control
ISSN号0885-7474
DOI10.1007/s10915-015-0051-2
英文摘要Finite 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.
资助项目Alexander 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研究方向Mathematics
语种英语
WOS记录号WOS:000369911500003
出版者SPRINGER/PLENUM PUBLISHERS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/22008]  
专题计算数学与科学工程计算研究所
通讯作者Gong, Wei
作者单位1.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
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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