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

doi:10.1007/s10915-015-0051-2

	Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs
	Gong, Wei1 ; Hinze, Michael 2; Zhou, Zhaojie 3
	2016-03-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	66 期号:3 页码:941-967
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.
关键词	Optimal control problem Parabolic equation Finite element method A priori error estimate Dirichlet boundary control
DOI	10.1007/s10915-015-0051-2
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000369911500003
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22009
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.