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Finite element approximation of optimal control problems governed by time fractional diffusion equation
Zhou, Zhaojie1; Gong, Wei2
2016
Source PublicationCOMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN0898-1221
Volume71Issue:1Pages:301-318
AbstractIn 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.
KeywordGalerkin finite element method Optimal control problems Time fractional diffusion equations A priori error estimate Variational discretization
DOI10.1016/j.camwa.2015.11.014
Language英语
Funding ProjectNational 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 AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000369455000020
PublisherPERGAMON-ELSEVIER SCIENCE LTD
Citation statistics
Cited Times:19[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21906
Collection计算数学与科学工程计算研究所
Affiliation1.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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