Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems
文献类型：期刊论文
| 作者 | Gong, Wei1 ; Xie, Hehu1,2; Yan, Ningning3
|
| 刊名 | JOURNAL OF SCIENTIFIC COMPUTING
 |
| 出版日期 | 2017-08-01 |
| 卷号 | 72期号:2页码:820-841 |
| 关键词 | Optimal control problems Elliptic equation Control constraints A posteriori error estimates Adaptive finite element method Multilevel correction method |
| ISSN号 | 0885-7474 |
| DOI | 10.1007/s10915-017-0386-y |
| 英文摘要 | In this paper we propose an adaptive multilevel correction scheme to solve optimal control problems discretized with finite element method. Different from the classical adaptive finite element method (AFEM for short) applied to optimal control which requires the solution of the optimization problem on new finite element space after each mesh refinement, with our approach we only need to solve two linear boundary value problems on current refined mesh and an optimization problem on a very low dimensional space. The linear boundary value problems can be solved with well-established multigrid method designed for elliptic equation and the optimization problems are of small scale corresponding to the space built with the coarsest space plus two enriched bases. Our approach can achieve the similar accuracy with standard AFEM but greatly reduces the computational cost. Numerical experiments demonstrate the efficiency of our proposed algorithm. |
| 资助项目 | 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[91330202] ; National Natural Science Foundation of China[11371026] ; National Natural Science Foundation of China[11001259] ; National Natural Science Foundation of China[11031006] ; National Natural Science Foundation of China[2011CB309703] ; National Natural Science Foundation of China[11571356] ; Science Challenge Project[JCKY2016212A502] ; National Center for Mathematics and Interdisciplinary Science, CAS ; President Foundation of AMSS-CAS |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000406014800015 |
| 出版者 | SPRINGER/PLENUM PUBLISHERS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/26115]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Gong, Wei |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.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,Xie, Hehu,Yan, Ningning. Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems[J]. JOURNAL OF SCIENTIFIC COMPUTING,2017,72(2):820-841. |
| APA | Gong, Wei,Xie, Hehu,&Yan, Ningning.(2017).Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems.JOURNAL OF SCIENTIFIC COMPUTING,72(2),820-841. |
| MLA | Gong, Wei,et al."Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems".JOURNAL OF SCIENTIFIC COMPUTING 72.2(2017):820-841. |
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。