Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations

doi:10.4208/nmtma.OA-2021-0123

CSpace

	Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations
	Liang, Dongdong 1; Gong, Wei 2,3; Xie, Xiaoping 1
	2021-12-23
发表期刊	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN	1004-8979
页码	35
摘要	In this paper, we consider parabolic distributed control problems with cost functional of pointwise observation type either in space or in time. First, we show the well-posedness of the optimization problems and derive the first order optimality systems, where the adjoint state can be expressed as the linear combination of solutions to two backward parabolic equations that involve the Dirac delta distribution as source either in space or in time. Second, we use a space-time finite element method to discretize the control problems, where the state variable is approximated by piecewise constant functions in time and continuous piecewise linear polynomials in space, and the control variable is discretized by following the variational discretization concept. We obtain a priori error estimates for the control and state variables with order O(k12 + h) up to a logarithmic factor under the L2-norm. Finally, we perform several numerical experiments to support our theoretical results.
关键词	Parabolic optimal control problem pointwise observation space-time finite element method parabolic PDE with Dirac measure error estimate
DOI	10.4208/nmtma.OA-2021-0123
收录类别	SCI
语种	英语
资助项目	Strategic Priority Research Program of Chi-nese Academy of Sciences[XDB 41000000] ; National Key Basic Research Program[2018YFB0704304] ; National Natural Science Foundation of China[12171340] ; National Natural Science Foundation of China[11771312]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000734869900001
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59812
专题	中国科学院数学与系统科学研究院
通讯作者	Gong, Wei
作者单位	1.Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liang, Dongdong,Gong, Wei,Xie, Xiaoping. Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2021:35.
APA	Liang, Dongdong,Gong, Wei,&Xie, Xiaoping.(2021).Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,35.
MLA	Liang, Dongdong,et al."Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS (2021):35.