Weak boundary penalization for Dirichlet boundary control problems governed by elliptic equations

doi:10.1016/j.jmaa.2017.04.016

	Weak boundary penalization for Dirichlet boundary control problems governed by elliptic equations
	Chang, Lili 1; Gong, Wei2 ; Yan, Ningning3
	2017-09-01
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	453 期号:1 页码:529-557
摘要	This paper concerns the finite element approximation of Dirichlet boundary control problems governed by elliptic equations. Different from the existing literatures, in which standard finite element method, mixed finite element method or Robin penalization method are used to deal with the underlying problems, we adopt an alternative penalization approach introduced by Nitsche called weak boundary penalization. Compared with the above methods, our discrete scheme not only keeps consistency and avoids penalization error, but also can be analyzed and computed conveniently as Neumann boundary control problems. Based on the weak boundary penalization method, we establish a finite element approximation to the Dirichlet boundary control problems and derive the a priori error estimates for the control, state and adjoint state. Numerical experiments are provided to confirm our theoretical results. (C) 2017 Elsevier Inc. All rights reserved.
关键词	Dirichlet boundary control Weak boundary penalization Finite element method A priori error estimate
DOI	10.1016/j.jmaa.2017.04.016
语种	英语
资助项目	Tianyuan Youth Fund of Mathematics of China[11526129] ; Youth Science Fund of Shanxi Province[2015021020]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000401782800033
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25350
专题	计算数学与科学工程计算研究所系统科学研究所
通讯作者	Chang, Lili
作者单位	1.Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Shanxi, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, LSEC,NCMIS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Chang, Lili,Gong, Wei,Yan, Ningning. Weak boundary penalization for Dirichlet boundary control problems governed by elliptic equations[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2017,453(1):529-557.
APA	Chang, Lili,Gong, Wei,&Yan, Ningning.(2017).Weak boundary penalization for Dirichlet boundary control problems governed by elliptic equations.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,453(1),529-557.
MLA	Chang, Lili,et al."Weak boundary penalization for Dirichlet boundary control problems governed by elliptic equations".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 453.1(2017):529-557.