A PRIORI ERROR ESTIMATE AND SUPERCONVERGENCE ANALYSIS FOR AN OPTIMAL CONTROL PROBLEM OF BILINEAR TYPE  

作　　者：Danping Yang Yanzhen Chang Wenbin Liu 

机构地区：[1]Department of Mathematics, East China Normal University, Shanghai 200062, China [2]School of Mathematics and System Science, Shandong University, Jinan 250100, China [3]KBS, University of Kent, Canterbury, CT2 7PE, England

出　　处：《Journal of Computational Mathematics》2008年第4期471-487,共17页计算数学（英文）

基　　金：the National Basic Research Program under the Grant 2005CB321703;the NSFC under the Grants 10571108 and 10441005;the Research Fund for Doctoral Program of High Education by China State Education Ministry under the Grant 2005042203

摘　　要：In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.

关 键 词：Bilinear control problem Finite element approximation SUPERCONVERGENCE Apriori error estimate A posteriori error estimator. 

分 类 号：O241[理学—计算数学]