Superconvergence of RT1 mixed finite element approximations for elliptic control problems  

作　　者：HOU TianLiang CHEN YanPing 

机构地区：[1]Department of Mathematics,Xiangtan University [2]School of Mathematical Sciences,South China Normal University

出　　处：《Science China Mathematics》2013年第2期267-281,共15页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.10971074);Foundation for Talent Introduction of Guangdong Provincial University,Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008);Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20114407110009)

摘　　要：In this paper,we investigate the superconvergence property of the numerical solution to a quadratic elliptic control problem by using mixed finite element methods.The state and co-state are approximated by the order k=1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We prove the superconvergence error estimate of h3/2 in L2-norm between the approximated solution and the average L2 projection of the control.Moreover,by the postprocessing technique,a quadratic superconvergence result of the control is derived.In this paper, we investigate the superconvergence property of the numerical solution to a quadratic elliptic control problem by using mixed finite element methods. The state and co-state are approximated by the order k = 1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We prove the superconvergence error estimate of h^3/2 in L^2-norm between the approximated solution and the average L2 projection of the control. Moreover, by the postprocessing technique, a quadratic superconvergence result of the control is derived.

关 键 词：elliptic equations optimal control problems SUPERCONVERGENCE mixed finite element methods POSTPROCESSING 

分 类 号：O241.82[理学—计算数学]