KMS Of Academy of mathematics and systems sciences, CAS
| A convergent adaptive finite element method for elliptic Dirichlet boundary control problems | |
Gong, Wei1 ; Liu, Wenbin2; Tan, Zhiyu3; Yan, Ningning4
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| 2019-10-01 | |
| Source Publication | IMA JOURNAL OF NUMERICAL ANALYSIS
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| ISSN | 0272-4979 |
| Volume | 39Issue:4Pages:1985-2015 |
| Abstract | 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. |
| Keyword | optimal control problem elliptic equation Dirichlet boundary control energy space adaptive finite element method convergence |
| DOI | 10.1093/imanum/dry051 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11671391] ; National Natural Science Foundation of China[91530204] ; National Natural Science Foundation of China[11571356] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000491253300013 |
| Publisher | OXFORD UNIV PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://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 Author | Gong, Wei |
| Affiliation | 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 |
| 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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