KMS Of Academy of mathematics and systems sciences, CAS
| Adaptive finite element method for elliptic optimal control problems: convergence and optimality | |
Gong, Wei1 ; Yan, Ningning2
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| 2017-04-01 | |
| Source Publication | NUMERISCHE MATHEMATIK
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| ISSN | 0029-599X |
| Volume | 135Issue:4Pages:1121-1170 |
| Abstract | In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and piecewise linear and continuous finite elements to approximate the state variable. Based on the well-established convergence theory of AFEM for elliptic boundary value problems, we rigorously prove the convergence and quasi-optimality of AFEM for optimal control problems with respect to the state and adjoint state variables, by using the so-called perturbation argument. Numerical experiments confirm our theoretical analysis. |
| DOI | 10.1007/s00211-016-0827-9 |
| Language | 英语 |
| Funding Project | National Basic Research Program of China[2012CB821204] ; National Natural Science Foundation of China[11201464] ; National Natural Science Foundation of China[91530204] ; National Natural Science Foundation of China[11171337] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000398175500006 |
| Publisher | SPRINGER HEIDELBERG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/25195 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Gong, Wei |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, NCMIS,LSEC, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Gong, Wei,Yan, Ningning. Adaptive finite element method for elliptic optimal control problems: convergence and optimality[J]. NUMERISCHE MATHEMATIK,2017,135(4):1121-1170. |
| APA | Gong, Wei,&Yan, Ningning.(2017).Adaptive finite element method for elliptic optimal control problems: convergence and optimality.NUMERISCHE MATHEMATIK,135(4),1121-1170. |
| MLA | Gong, Wei,et al."Adaptive finite element method for elliptic optimal control problems: convergence and optimality".NUMERISCHE MATHEMATIK 135.4(2017):1121-1170. |
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