Finite element approximation of optimal control problems governed by time fractional diffusion equation

doi:10.1016/j.camwa.2015.11.014

	Finite element approximation of optimal control problems governed by time fractional diffusion equation
	Zhou, Zhaojie 1; Gong, Wei2
	2016
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	71 期号:1 页码:301-318
摘要	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.
关键词	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
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000369455000020
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21906
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Zhaojie
作者单位	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
推荐引用方式 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.