RICHARDSON EXTRAPOLATION AND DEFECT CORRECTION OF FINITE ELEMENT METHODS FOR OPTIMAL CONTROL PROBLEMS  

作　　者：Tang Liu Ningning Yan Shuhua Zhang 

机构地区：[1]Research Center for Mathematics and Economics Tianjin University of Finance and Economics, Tianjin 300222, China [2]Institute of System Sciences, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Journal of Computational Mathematics》2010年第1期55-71,共17页计算数学（英文）

基　　金：supported in part by the National Basic Research Program (2007CB814906);the National Natural Science Foundation of China (10471103 and 10771158);Social Science Foundation of the Ministry of Education of China (06JA630047);Tianjin Natural Science Foundation (07JCYBJC14300);Tianjin University of Finance and Economics;supported by the National Basic Research Program under the Grant 2005CB321701;the National Natural Science Foundation of China under the Grant 10771211

摘　　要：Asymptotic error expansions in H^1-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectan- gular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation.Asymptotic error expansions in H^1-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectan- gular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation.

关 键 词：Optimal control problem Finite element methods Asymptotic error expansions Defect correction A posteriori error estimates. 

分 类 号：O232[理学—运筹学与控制论] S965.325[理学—数学]