标题:A PRIORI ERROR ESTIMATES FOR LEAST-SQUARES MIXED FINITE ELEMENT APPROXIMATION OF ELLIPTIC OPTIMAL CONTROL PROBLEMS
作者:Fu, Hongfei; Rui, Hongxing
作者机构:[Fu, H] College of Science, China University of Petroleum, Qingdao, 266580, China;[ Rui, H] School of Mathematics, Shandong University, Jinan, 250100, 更多
通讯作者:Fu, HF
通讯作者地址:[Fu, HF]China Univ Petr, Coll Sci, Qingdao 266580, Peoples R China.
来源:计算数学(英文版)
出版年:2015
卷:33
期:2
页码:113-127
DOI:10.4208/jcm.1406-m4396
关键词:Optimal control; Least-squares mixed finite element methods; First-order; elliptic system; A priori error estimates
摘要:In this paper, a constrained distributed optimal control problem governed by a first-order elliptic system is considered. Least-squares mixed finite element methods, which are not subject to the Ladyzhenkaya-Babuska-Brezzi consistency condition, are used for solving the elliptic system with two unknown state variables. By adopting the Lagrange multiplier approach, continuous and discrete optimality systems including a primal state equation, an adjoint state equation, and a variational inequality for the optimal control are derived, respectively. Both the discrete state equation and discrete adjoint state equation yield a symmetric and positive definite linear algebraic system. Thus, the popular solvers such as preconditioned conjugate gradient (PCG) and algebraic multi-grid (AMG) can be used for rapid solution. Optimal a priori error estimates are obtained, respectively, for the control function in L-2(Omega)-norm, for the original state and adjoint state in H-1(Omega)-norm, and for the flux state and adjoint flux state in H(div;Omega)-norm. Finally, we use one numerical example to validate the theoretical findings.
收录类别:SCOPUS;SCIE
WOS核心被引频次:2
Scopus被引频次:2
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-84929625481&doi=10.4208%2fjcm.1406-m4396&partnerID=40&md5=c6c8ff1c4b23c6ca9f949d470b24e74e
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