A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations  

作　　者：Tianliang Hou Yanping Chen Yunqing Huang 

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

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2011年第4期439-458,共20页高等学校计算数学学报（英文版）

基　　金：supported in part by Hunan Education Department Key Project 10A117 and Hunan Provincial Innovation Foundation for Postgraduate CX2010B247;supported by the Foundation for Talent Introduction of Guangdong Provincial University,Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008)and National Science Foundation of China(10971074);supported in part by the NSFC Key Project(11031006);Hunan Provincial NSF Project(10JJ7001);the NSFC for Distinguished Young Scholars(10625106);National Basic Research Program of China under the Grant 2005 CB321701.

摘　　要：In this paper,we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations.The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.We derive a posteriori error estimates for both the state and the control approximation.Such estimates,which are apparently not available in the literature,are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

关 键 词：A posteriori error estimates quadratic optimal control problems parabolic equations mixed finite element methods 

分 类 号：O17[理学—数学]