KMS Of Academy of mathematics and systems sciences, CAS
| Finite element approximation of optimal control problems governed by time fractional diffusion equation | |
Zhou, Zhaojie1; Gong, Wei2
| |
| 2016 | |
| Source Publication | COMPUTERS & MATHEMATICS WITH APPLICATIONS
 |
| ISSN | 0898-1221 |
| Volume | 71Issue:1Pages:301-318 |
| Abstract | In this paper Galerkin finite element approximation of optimal control problems governed by time fractional diffusion equations is investigated. Piecewise linear polynomials are used to approximate the state and adjoint state, while the control is discretized by variational discretization method. A priori error estimates for the semi-discrete approximations of the state, adjoint state and control are derived. Furthermore, we also discuss the fully discrete scheme for the control problems. A finite difference method developed in Lin and Xu (2007) is used to discretize the time fractional derivative. Fully discrete first order optimality condition is developed based on 'first discretize, then optimize' approach. The stability and truncation error of the fully discrete scheme are analyzed. Numerical example is given to illustrate the theoretical findings. (C) 2015 Elsevier Ltd. All rights reserved. |
| Keyword | Galerkin finite element method Optimal control problems Time fractional diffusion equations A priori error estimate Variational discretization |
| DOI | 10.1016/j.camwa.2015.11.014 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11301311] ; National Natural Science Foundation of China[11471196] ; National Natural Science Foundation of China[11201464] ; National Natural Science Foundation of China[91330115] ; National Basic Research Program of China[2012CB821204] ; scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000369455000020 |
| Publisher | PERGAMON-ELSEVIER SCIENCE LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/21906 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Zhou, Zhaojie |
| Affiliation | 1.Shandong Normal Univ, Coll Math Sci, Jinan 250014, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Zhou, Zhaojie,Gong, Wei. Finite element approximation of optimal control problems governed by time fractional diffusion equation[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2016,71(1):301-318. |
| APA | Zhou, Zhaojie,&Gong, Wei.(2016).Finite element approximation of optimal control problems governed by time fractional diffusion equation.COMPUTERS & MATHEMATICS WITH APPLICATIONS,71(1),301-318. |
| MLA | Zhou, Zhaojie,et al."Finite element approximation of optimal control problems governed by time fractional diffusion equation".COMPUTERS & MATHEMATICS WITH APPLICATIONS 71.1(2016):301-318. |
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