Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problem

doi:10.1016/j.cam.2019.01.038

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	Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problem
	Shen, Yue 1; Yan, Ningning2,3 ; Zhou, Zhaojie 4
	2019-08-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	356 页码:1-21
摘要	In this paper we focus on the convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problems. We use piecewise linear finite elements to approximate the state and the adjoint state variables, and the variational discretization to approximate the control variable. Under mild assumption on the initial mesh, we prove the contraction property, for the sum of the energy errors of the state and adjoint state and the scaled error estimator, on two consecutive adaptive loops. The resulting linear convergence yields the quasi-optimal convergence rate for the AFEM algorithm applied to our problem. Additionally, some numerical results are provided to support our theoretical analysis. (C) 2019 Elsevier B.V. All rights reserved.
关键词	Elliptic optimal control problem Robin boundary control Adaptive finite element method Convergence and quasi-optimality
DOI	10.1016/j.cam.2019.01.038
语种	英语
资助项目	National Natural Science Foundation of China[11301311] ; Natural Science Foundation of Shandong Province[ZR2016JL004]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000463693100001
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34435
专题	系统科学研究所
通讯作者	Zhou, Zhaojie
作者单位	1.Univ Chinese Acad Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, NCMIS,LSEC, Beijing 100190, Peoples R China 4.Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Shandong, Peoples R China
推荐引用方式 GB/T 7714	Shen, Yue,Yan, Ningning,Zhou, Zhaojie. Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problem[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2019,356:1-21.
APA	Shen, Yue,Yan, Ningning,&Zhou, Zhaojie.(2019).Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problem.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,356,1-21.
MLA	Shen, Yue,et al."Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problem".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 356(2019):1-21.