Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problem
文献类型：期刊论文
| 作者 | Shen, Yue2; Yan, Ningning1,3 ; Zhou, Zhaojie4
|
| 刊名 | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
 |
| 出版日期 | 2019-08-15 |
| 卷号 | 356页码:1-21 |
| 关键词 | Elliptic optimal control problem Robin boundary control Adaptive finite element method Convergence and quasi-optimality |
| ISSN号 | 0377-0427 |
| DOI | 10.1016/j.cam.2019.01.038 |
| 英文摘要 | 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. |
| 资助项目 | National Natural Science Foundation of China[11301311] ; Natural Science Foundation of Shandong Province[ZR2016JL004] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000463693100001 |
| 出版者 | ELSEVIER SCIENCE BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/34434]  |
| 专题 | 系统科学研究所 |
| 通讯作者 | Zhou, Zhaojie |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, NCMIS,LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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