A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems

查看全文 作　　者：Wanfang [1]Shen;Liang [2]Ge;Danping [3]Yang;Wenbin [4]Liu 机构地区：[1]School of Mathematic and Quantitative Economics,Shandong University of Finance and Economics,Jinan 250014,China;[2]Shandong Provincial Key Laboratory of Computer Network,Shandong Computer Science Center,Jinan 250014,China;[3]Department of Mathematics,East China Normal University,Shanghai 200241,China;[4]KBS,University of Kent,Canterbury,CT27NF,England 出　　处：《Advances in Applied Mathematics and Mechanics》索引2014年第6卷第5期,共18页 基　　金：W.F.Shen was supported by National Natural Science Foundation of China(Grant:11326226);Nature Science Foundation of Shandong Province(No.ZR2012GM018);D.P.Yang partially was supported by National Natural Science Foundation of China,Grant:11071080. 摘　　要：In this paper,we study the mathematical formulation for an optimal control problem governed by a linear parabolic integro-differential equation and present the optimality conditions.We then set up its weak formulation and the finite element approximation scheme.Based on these we derive the a priori error estimates for its finite element approximation both in H1 and L^(2)norms.Furthermore some numerical tests are presented to verify the theoretical results. 关 键 词：Optimal control linear parabolic integro-differential equations optimality conditions finite element methods a priori error estimate.