A mixed multiscale finite element method for convex optimal control problems with oscillating coefficients

doi:10.1016/j.camwa.2015.03.020

CSpace > 系统科学研究所

	A mixed multiscale finite element method for convex optimal control problems with oscillating coefficients
	Chen, Yanping 1; Huang, Yunqing 2,3; Liu, Wenbin 4,5; Yan, Ningning6
	2015-08-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	70 期号:4 页码:297-313
摘要	We study numerical approximation of convex optimal control problems governed by elliptic partial differential equations with oscillating coefficients. Since the objective functional contains flux, we approximate the problems using the mixed finite element methods. We first analyze the standard mixed finite element approximation schemes. Then, motivated by the numerical simulation of the primal variable and the flux in highly heterogeneous porous media, we use a multiscale mixed finite element method to solve the state equations. The multiscale finite element bases are constructed by locally solving Neumann boundary value problems. The analysis of the approximate control problems is carried out under the assumption that the oscillating coefficients are locally periodic, which allows us to use homogenization theory to obtain the asymptotic structure of the solutions, although the numerical schemes are designed for the general case. (C) 2015 Elsevier Ltd. All rights reserved.
关键词	Multiscale control problem Mixed finite element Homogenization A prior error estimates
DOI	10.1016/j.camwa.2015.03.020
语种	英语
资助项目	National Science Foundation of China[91430104] ; National Science Foundation of China[11271145] ; National Science Foundation of China[91430213] ; Specialized Research Fund for the Doctoral Program of Higher Education[20114407110009]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000359963200001
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/20594
专题	系统科学研究所
通讯作者	Chen, Yanping
作者单位	1.S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China 2.Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China 3.Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China 4.Univ Kent, KBS, Canterbury CT2 7NF, Kent, England 5.Univ Kent, IMS, Canterbury CT2 7NF, Kent, England 6.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Chen, Yanping,Huang, Yunqing,Liu, Wenbin,et al. A mixed multiscale finite element method for convex optimal control problems with oscillating coefficients[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2015,70(4):297-313.
APA	Chen, Yanping,Huang, Yunqing,Liu, Wenbin,&Yan, Ningning.(2015).A mixed multiscale finite element method for convex optimal control problems with oscillating coefficients.COMPUTERS & MATHEMATICS WITH APPLICATIONS,70(4),297-313.
MLA	Chen, Yanping,et al."A mixed multiscale finite element method for convex optimal control problems with oscillating coefficients".COMPUTERS & MATHEMATICS WITH APPLICATIONS 70.4(2015):297-313.