Adaptive finite element method for elliptic optimal control problems: convergence and optimality

doi:10.1007/s00211-016-0827-9

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Adaptive finite element method for elliptic optimal control problems: convergence and optimality
	Gong, Wei1 ; Yan, Ningning2
刊名	NUMERISCHE MATHEMATIK
	2017-04-01
卷号	135 期号:4 页码:1121-1170
ISSN号	0029-599X
DOI	10.1007/s00211-016-0827-9
英文摘要	In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and piecewise linear and continuous finite elements to approximate the state variable. Based on the well-established convergence theory of AFEM for elliptic boundary value problems, we rigorously prove the convergence and quasi-optimality of AFEM for optimal control problems with respect to the state and adjoint state variables, by using the so-called perturbation argument. Numerical experiments confirm our theoretical analysis.
资助项目	National Basic Research Program of China[2012CB821204] ; National Natural Science Foundation of China[11201464] ; National Natural Science Foundation of China[91530204] ; National Natural Science Foundation of China[11171337]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000398175500006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/25194]
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, NCMIS,LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, NCMIS,LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Gong, Wei,Yan, Ningning. Adaptive finite element method for elliptic optimal control problems: convergence and optimality[J]. NUMERISCHE MATHEMATIK,2017,135(4):1121-1170.
APA	Gong, Wei,&Yan, Ningning.(2017).Adaptive finite element method for elliptic optimal control problems: convergence and optimality.NUMERISCHE MATHEMATIK,135(4),1121-1170.
MLA	Gong, Wei,et al."Adaptive finite element method for elliptic optimal control problems: convergence and optimality".NUMERISCHE MATHEMATIK 135.4(2017):1121-1170.