Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations
文献类型：期刊论文
| 作者 | Liang, Dongdong1; Gong, Wei2,3; Xie, Xiaoping1 |
| 刊名 | NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
 |
| 出版日期 | 2021-12-23 |
| 页码 | 35 |
| ISSN号 | 1004-8979 |
| 关键词 | 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 |
| 英文摘要 | 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. |
| 资助项目 | 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研究方向 | Mathematics |
| 语种 | 英语 |
| 出版者 | GLOBAL SCIENCE PRESS |
| WOS记录号 | WOS:000734869900001 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59811]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Gong, Wei |
| 作者单位 | 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 |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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