A convergent adaptive finite element method for elliptic Dirichlet boundary control problems

doi:10.1093/imanum/dry051

	A convergent adaptive finite element method for elliptic Dirichlet boundary control problems
	Gong, Wei1 ; Liu, Wenbin 2; Tan, Zhiyu 3; Yan, Ningning4
	2019-10-01
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	39 期号:4 页码:1985-2015
摘要	This paper concerns the adaptive finite element method for elliptic Dirichlet boundary control problems in the energy space. The contribution of this paper is twofold. First, we rigorously derive efficient and reliable a posteriori error estimates for finite element approximations of Dirichlet boundary control problems. As a by-product, a priori error estimates are derived in a simple way by introducing appropriate auxiliary problems and establishing certain norm equivalence. Secondly, for the coupled elliptic partial differential system that resulted from the first-order optimality system, we prove that the sequence of adaptively generated discrete solutions including the control, the state and the adjoint state, guided by our newly derived a posteriori error indicators, converges to the true solution along with the convergence of the error estimators. We give some numerical results to confirm our theoretical findings.
关键词	optimal control problem elliptic equation Dirichlet boundary control energy space adaptive finite element method convergence
DOI	10.1093/imanum/dry051
语种	英语
资助项目	National Natural Science Foundation of China[11671391] ; National Natural Science Foundation of China[91530204] ; National Natural Science Foundation of China[11571356]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000491253300013
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35975
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	Gong, Wei
作者单位	1.Chinese Acad Sci, Natl Ctr Math & Interdisciplinary Sci, State Key Lab Sci & Engn Comp, Inst Computat Math,Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Kent, Kent Business Sch, Canterbury CT2 7PE, Kent, England 3.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 4.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,Liu, Wenbin,Tan, Zhiyu,et al. A convergent adaptive finite element method for elliptic Dirichlet boundary control problems[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2019,39(4):1985-2015.
APA	Gong, Wei,Liu, Wenbin,Tan, Zhiyu,&Yan, Ningning.(2019).A convergent adaptive finite element method for elliptic Dirichlet boundary control problems.IMA JOURNAL OF NUMERICAL ANALYSIS,39(4),1985-2015.
MLA	Gong, Wei,et al."A convergent adaptive finite element method for elliptic Dirichlet boundary control problems".IMA JOURNAL OF NUMERICAL ANALYSIS 39.4(2019):1985-2015.