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

作　　者：Hong-bo GUAN Dong-yang SHI 

机构地区：[1]College of Mathematics and Information Sciences,Zhengzhou University of Light Industry,Zhengzhou 450002,China [2]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第2期471-481,共11页应用数学学报（英文版）

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

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 control.Firstly,the convergence and superconvergence properties for the nonsmooth elliptic equation are obtained by introducing an auxiliary problem.Secondly,the goal-oriented error estimates are obtained for the objective function through establishing the negative norm error estimate.Lastly,the methods are extended to some other well-known nonconforming elements.

关 键 词：NONCONFORMING finite element SUPERCLOSENESS and SUPERCONVERGENCE optimal control problems NONSMOOTH ELLIPTIC equations goal-oriented error estimate 

分 类 号：O232[理学—运筹学与控制论]