Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems

doi:10.1007/s10915-017-0386-y

	Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems
	Gong, Wei1 ; Xie, Hehu1,2 ; Yan, Ningning3
	2017-08-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	72 期号:2 页码:820-841
摘要	In this paper we propose an adaptive multilevel correction scheme to solve optimal control problems discretized with finite element method. Different from the classical adaptive finite element method (AFEM for short) applied to optimal control which requires the solution of the optimization problem on new finite element space after each mesh refinement, with our approach we only need to solve two linear boundary value problems on current refined mesh and an optimization problem on a very low dimensional space. The linear boundary value problems can be solved with well-established multigrid method designed for elliptic equation and the optimization problems are of small scale corresponding to the space built with the coarsest space plus two enriched bases. Our approach can achieve the similar accuracy with standard AFEM but greatly reduces the computational cost. Numerical experiments demonstrate the efficiency of our proposed algorithm.
关键词	Optimal control problems Elliptic equation Control constraints A posteriori error estimates Adaptive finite element method Multilevel correction method
DOI	10.1007/s10915-017-0386-y
语种	英语
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[91330202] ; National Natural Science Foundation of China[11371026] ; National Natural Science Foundation of China[11001259] ; National Natural Science Foundation of China[11031006] ; National Natural Science Foundation of China[2011CB309703] ; National Natural Science Foundation of China[11571356] ; Science Challenge Project[JCKY2016212A502] ; National Center for Mathematics and Interdisciplinary Science, CAS ; President Foundation of AMSS-CAS
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000406014800015
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/26116
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, 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	Gong, Wei,Xie, Hehu,Yan, Ningning. Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems[J]. JOURNAL OF SCIENTIFIC COMPUTING,2017,72(2):820-841.
APA	Gong, Wei,Xie, Hehu,&Yan, Ningning.(2017).Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems.JOURNAL OF SCIENTIFIC COMPUTING,72(2),820-841.
MLA	Gong, Wei,et al."Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems".JOURNAL OF SCIENTIFIC COMPUTING 72.2(2017):820-841.