A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations  

作　　者：CHEN YanPing HUANG YunQing YI NianYu 

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China [2]Hunan Key Laboratory for Computation and Simulation in Science and Engineering,School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China

出　　处：《Science China Mathematics》2008年第8期1376-1390,共15页中国科学：数学（英文版）

基　　金：the National Basic Research Program;the National Natural Science Foundation of China(Grant No.2005CB321703);Scientific Research Fund of Hunan Provincial Education Department;the Outstanding Youth Scientist of the National Natural Science Foundation of China(Grant No.10625106);the National Basic Research Program of China(Grant No.2005CB321701)

摘　　要：In this paper,we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations.A spectral approximation scheme for the parabolic optimal control problem is presented.We obtain a posteriori error estimates of the approximated solutions for both the state and the control.In this paper, we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations. A spectral approximation scheme for the parabolic optimal control problem is presented. We obtain a posteriori error estimates of the approximated solutions for both the state and the control.

关 键 词：Legendre Galerkin spectral method optimal control problems parabolic state equations a posteriori error estimates 49J20 65M60 65M70 

分 类 号：O232[理学—运筹学与控制论]