KMS Of Academy of mathematics and systems sciences, CAS
| Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations | |
| Liang, Dongdong1; Gong, Wei2,3; Xie, Xiaoping1 | |
| 2021-12-23 | |
| Source Publication | NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
 |
| ISSN | 1004-8979 |
| Pages | 35 |
| Abstract | In this paper, we consider parabolic distributed control problems with cost functional of pointwise observation type either in space or in time. First, we show the well-posedness of the optimization problems and derive the first order optimality systems, where the adjoint state can be expressed as the linear combination of solutions to two backward parabolic equations that involve the Dirac delta distribution as source either in space or in time. Second, we use a space-time finite element method to discretize the control problems, where the state variable is approximated by piecewise constant functions in time and continuous piecewise linear polynomials in space, and the control variable is discretized by following the variational discretization concept. We obtain a priori error estimates for the control and state variables with order O(k12 + h) up to a logarithmic factor under the L2-norm. Finally, we perform several numerical experiments to support our theoretical results. |
| Keyword | Parabolic optimal control problem pointwise observation space-time finite element method parabolic PDE with Dirac measure error estimate |
| DOI | 10.4208/nmtma.OA-2021-0123 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | Strategic Priority Research Program of Chi-nese Academy of Sciences[XDB 41000000] ; National Key Basic Research Program[2018YFB0704304] ; National Natural Science Foundation of China[12171340] ; National Natural Science Foundation of China[11771312] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000734869900001 |
| Publisher | GLOBAL SCIENCE PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59812 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Gong, Wei |
| Affiliation | 1.Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Liang, Dongdong,Gong, Wei,Xie, Xiaoping. Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2021:35. |
| APA | Liang, Dongdong,Gong, Wei,&Xie, Xiaoping.(2021).Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,35. |
| MLA | Liang, Dongdong,et al."Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS (2021):35. |
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