SUPERCONVERGENCE ANALYSIS OF FINITE ELEMENT METHODS FOR OPTIMAL CONTROL PROBLEMS OF THE STATIONARY B(?)NARD TYPE

作     者：Yanzhen Chang Danping Yang 

作者机构：School of Mathematics and System Science Shandong University Jinan 250100 China Department of Mathematics East China Normal University Shanghai 200062 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2008年第26卷第5期

页      面：660-676页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：the Research Fund for Doctoral Program of High Education by China State Education Ministry under the Grant 2005042203 

主　　题：Optimal control problem The stationary Benard problem Nonlinear coupled system Finite element approximation Superconvergence. 

摘      要：In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Benard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the superconvergence analysis for the control; it is proved that the approximation has a second-order rate of convergence. We further give the superconvergence analysis for the states and the co-states. Then we derive error estimates in L^∞-norm and optimal error estimates in L^2-norm.