FINITE ELEMENT APPROXIMATIONS OF PARABOLIC OPTIMAL CONTROL PROBLEMS WITH CONTROLS ACTING ON A LOWER DIMENSIONAL MANIFOLD

doi:10.1137/151004744

	FINITE ELEMENT APPROXIMATIONS OF PARABOLIC OPTIMAL CONTROL PROBLEMS WITH CONTROLS ACTING ON A LOWER DIMENSIONAL MANIFOLD
	Gong, Wei1 ; Yan, Ningning 2
	2016
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	54 期号:2 页码:1229-1262
摘要	This paper is devoted to the study of finite element approximations to parabolic optimal control problems with controls acting on a lower dimensional manifold. The manifold can be a point, a curve, or a surface which may be independent of time or evolve in the time horizon, and is assumed to be strictly contained in the space domain. At first, we obtain the first order optimality conditions for the control problems and the corresponding regularity results. Then, for the control problems we consider the fully discrete finite element approximations based on the piecewise constant discontinuous Galerkin scheme for time discretization and piecewise linear finite elements for space discretization, and variational discretization to the control variable. A priori error estimates are finally obtained for the fully discretized control problems and supported by numerical examples.
关键词	finite element method parabolic equation optimal control problem moving manifold fully discrete error estimates
DOI	10.1137/151004744
语种	英语
资助项目	National Basic Research Program of China[2012CB821204] ; National Natural Science Foundation of China[91530204] ; National Natural Science Foundation of China[11201464] ; National Natural Science Foundation of China[11571356] ; Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000375488100029
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22584
专题	计算数学与科学工程计算研究所
通讯作者	Gong, Wei; Yan, Ningning
作者单位	1.Chinese Acad Sci, NCMIS, LSEC, Inst Computat Math,Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, NCMIS, LSEC, Inst Syst Sci,Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Gong, Wei,Yan, Ningning. FINITE ELEMENT APPROXIMATIONS OF PARABOLIC OPTIMAL CONTROL PROBLEMS WITH CONTROLS ACTING ON A LOWER DIMENSIONAL MANIFOLD[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2016,54(2):1229-1262.
APA	Gong, Wei,&Yan, Ningning.(2016).FINITE ELEMENT APPROXIMATIONS OF PARABOLIC OPTIMAL CONTROL PROBLEMS WITH CONTROLS ACTING ON A LOWER DIMENSIONAL MANIFOLD.SIAM JOURNAL ON NUMERICAL ANALYSIS,54(2),1229-1262.
MLA	Gong, Wei,et al."FINITE ELEMENT APPROXIMATIONS OF PARABOLIC OPTIMAL CONTROL PROBLEMS WITH CONTROLS ACTING ON A LOWER DIMENSIONAL MANIFOLD".SIAM JOURNAL ON NUMERICAL ANALYSIS 54.2(2016):1229-1262.