Nonconforming Finite Element Methods for the Constrained Optimal Control Problems Governed by Nonsmooth Elliptic Equations

作     者：Hong-bo GUAN Dong-yang SHI Hong-bo GUAN;Dong-yang SHI

作者机构：College of Mathematics and Information SciencesZhengzhou University of Light IndustryZhengzhou 450002China School of Mathematics and StatisticsZhengzhou UniversityZhengzhou 450001China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2020年第36卷第2期

页      面：471-481页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.11501527 11671369) 

主　　题：nonconforming finite element supercloseness and superconvergence optimal control problems nonsmooth elliptic equations goal-oriented error estimate 

摘      要：In this paper,nonconforming finite element methods(FEMs)are proposed for the constrained optimal control problems(OCPs)governed by the nonsmooth elliptic equations,in which the popular EQr1 ot element is employed to approximate the state and adjoint state,and the piecewise constant element is used to approximate the ***,the convergence and superconvergence properties for the nonsmooth elliptic equation are obtained by introducing an auxiliary ***,the goal-oriented error estimates are obtained for the objective function through establishing the negative norm error ***,the methods are extended to some other well-known nonconforming elements.