Fully Discrete H^(1) -Galerkin Mixed Finite Element Methods for Parabolic Optimal Control Problems

作     者：Tianliang Hou Chunmei Liu Hongbo Chen 

作者机构：School of Mathematics and StatisticsNortheast Normal UniversityChangchun 130024China School of Mathematics and StatisticsBeihua UniversityJilin 132013China Institute for Computational MathematicsCollege of ScienceHunan University of Science and EngineeringYongzhou 425199HunanChina 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2019年第12卷第1期

页      面：134-153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：This work was supported by National Natural Science Foundation of China(11601014,11626037,11526036) China Postdoctoral Science Foundation(2016M 601359) Scientific and Technological Developing Scheme of Jilin Province(20160520108 JH,20170101037JC) Science and Technology Research Project of Jilin Provincial Depart-ment of Education(201646) Special Funding for Promotion of Young Teachers of Beihua University,Natural Science Foundation of Hunan Province(14JJ3135) the Youth Project of Hunan Provincial Education Department(15B096) the construct program of the key discipline in Hunan University of Science and Engineering 

主　　题：Parabolic equations optimal control problems a priori error estimates a posteriori error estimates H^(1)-Galerkin mixed finite element methods 

摘      要：In this paper,we investigate a priori and a posteriori error estimates of fully discrete H^(1)-Galerkin mixed finite element methods for parabolic optimal control *** state variables and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element and linear finite element,and the control vari-able is approximated by piecewise constant *** time discretization of the state and co-state are based on finite difference ***,we derive a priori error estimates for the control variable,the state variables and the adjoint state ***,by use of energy approach,we derive a posteriori error estimates for optimal control problems,assuming that only the underlying mesh is static.A numerical example is presented to verify the theoretical results on a priori error estimates.