KMS Of Academy of mathematics and systems sciences, CAS
| Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problem | |
Shen, Yue1; Yan, Ningning2,3 ; Zhou, Zhaojie4
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| 2019-08-15 | |
| Source Publication | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
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| ISSN | 0377-0427 |
| Volume | 356Pages:1-21 |
| Abstract | 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. |
| Keyword | Elliptic optimal control problem Robin boundary control Adaptive finite element method Convergence and quasi-optimality |
| DOI | 10.1016/j.cam.2019.01.038 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11301311] ; Natural Science Foundation of Shandong Province[ZR2016JL004] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000463693100001 |
| Publisher | ELSEVIER SCIENCE BV |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/34435 |
| Collection | 系统科学研究所 |
| Corresponding Author | Zhou, Zhaojie |
| Affiliation | 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 |
| Recommended Citation 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. |
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