Optimal convergence of finite element approximation to an optimization problem with PDE constraint*

doi:10.1088/1361-6420/ac4f5c

	Optimal convergence of finite element approximation to an optimization problem with PDE constraint*
	Gong, Wei 2,3; Tan, Zhiyu 4; Zhou, Zhaojie 1
刊名	INVERSE PROBLEMS
	2022-04-01
卷号	38 期号:4 页码:45
关键词	inverse source problem optimal control finite element method a priori error estimate a posteriori error estimate adaptivity rate optimality
ISSN号	0266-5611
DOI	10.1088/1361-6420/ac4f5c
英文摘要	We study in this paper the optimal convergence of finite element approximation to an optimization problem with PDE constraint. Specifically, we consider an elliptic distributed optimal control problem without control constraints, which can also be viewed as a regularized inverse source problem. The main contributions are two-fold. First, we derive a priori and a posteriori error estimates for the optimization problems, under an appropriately chosen norm that allows us to establish an isomorphism between the solution space and its dual. These results yield error estimates with explicit dependence on the regularization parameter alpha so that the constants appeared in the derivation are independent of alpha. Second, we prove the contraction property and rate optimality for the adaptive algorithm with respect to the error estimator and solution errors between the adaptive finite element solutions and the continuous solutions. Extensive numerical experiments are presented that confirm our theoretical results.
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	IOP Publishing Ltd
WOS记录号	WOS:000766855100001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60103]
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.Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Computat Math, Beijing 100190, Peoples R China 4.Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USA
推荐引用方式 GB/T 7714	Gong, Wei,Tan, Zhiyu,Zhou, Zhaojie. Optimal convergence of finite element approximation to an optimization problem with PDE constraint*[J]. INVERSE PROBLEMS,2022,38(4):45.
APA	Gong, Wei,Tan, Zhiyu,&Zhou, Zhaojie.(2022).Optimal convergence of finite element approximation to an optimization problem with PDE constraint*.INVERSE PROBLEMS,38(4),45.
MLA	Gong, Wei,et al."Optimal convergence of finite element approximation to an optimization problem with PDE constraint*".INVERSE PROBLEMS 38.4(2022):45.