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 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 China2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China Recommended CitationGB/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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