A convergent adaptive finite element method for elliptic Dirichlet boundary control problems
文献类型：期刊论文
| 作者 | Gong, Wei1 ; Liu, Wenbin2; Tan, Zhiyu3; Yan, Ningning4
|
| 刊名 | IMA JOURNAL OF NUMERICAL ANALYSIS
 |
| 出版日期 | 2019-10-01 |
| 卷号 | 39期号:4页码:1985-2015 |
| 关键词 | optimal control problem elliptic equation Dirichlet boundary control energy space adaptive finite element method convergence |
| ISSN号 | 0272-4979 |
| DOI | 10.1093/imanum/dry051 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000491253300013 |
| 出版者 | OXFORD UNIV PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/35974]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。