Numerical analysis for the approximation of optimal control problems with pointwise observations

doi:10.1002/mma.2861

	Numerical analysis for the approximation of optimal control problems with pointwise observations
	Chang, Lili 1; Gong, Wei2 ; Yan, Ningning3
	2015-12-01
发表期刊	MATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN	0170-4214
卷号	38 期号:18 页码:4502-4520
摘要	In this paper, we study the numerical methods for optimal control problems governed by elliptic PDEs with pointwise observations of the state. The first order optimality conditions as well as regularities of the solutions are derived. The optimal control and adjoint state have low regularities due to the pointwise observations. For the finite dimensional approximation, we use the standard conforming piecewise linear finite elements to approximate the state and adjoint state variables, whereas variational discretization is applied to the discretization of the control. A priori and a posteriori error estimates for the optimal control, the state and adjoint state are obtained. Numerical experiments are also provided to confirm our theoretical results. Copyright (C) 2013 John Wiley & Sons, Ltd.
关键词	optimal control problems pointwise observations finite element method a priori error estimate a posteriori error estimate
DOI	10.1002/mma.2861
语种	英语
资助项目	National Natural Science Foundation of China[11171337] ; National Natural Science Foundation of China[11201464] ; National Basic Research Program[2010CB731505] ; National Basic Research Program[2012CB821204]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000368252300005
出版者	WILEY-BLACKWELL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21753
专题	计算数学与科学工程计算研究所系统科学研究所
通讯作者	Chang, Lili
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 3.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	Chang, Lili,Gong, Wei,Yan, Ningning. Numerical analysis for the approximation of optimal control problems with pointwise observations[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2015,38(18):4502-4520.
APA	Chang, Lili,Gong, Wei,&Yan, Ningning.(2015).Numerical analysis for the approximation of optimal control problems with pointwise observations.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,38(18),4502-4520.
MLA	Chang, Lili,et al."Numerical analysis for the approximation of optimal control problems with pointwise observations".MATHEMATICAL METHODS IN THE APPLIED SCIENCES 38.18(2015):4502-4520.