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A convergent adaptive finite element method for elliptic Dirichlet boundary control problems
Gong, Wei1; Liu, Wenbin2; Tan, Zhiyu3; Yan, Ningning4
2019-10-01
Source PublicationIMA JOURNAL OF NUMERICAL ANALYSIS
ISSN0272-4979
Volume39Issue:4Pages:1985-2015
AbstractThis 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.
Keywordoptimal control problem elliptic equation Dirichlet boundary control energy space adaptive finite element method convergence
DOI10.1093/imanum/dry051
Language英语
Funding ProjectNational Natural Science Foundation of China[11671391] ; National Natural Science Foundation of China[91530204] ; National Natural Science Foundation of China[11571356]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000491253300013
PublisherOXFORD UNIV PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35975
Collection计算数学与科学工程计算研究所
系统科学研究所
Corresponding AuthorGong, Wei
Affiliation1.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
Recommended Citation
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.
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