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

被引：7
|
作者：
Shen, Wanfang [1 ]
Ge, Liang [2 ]
Yang, Danping [3 ]
Liu, Wenbin [4 ]
机构：
[1] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Peoples R China
[2] Shandong Comp Sci Ctr, Shandong Prov Key Lab Comp Network, Jinan 250014, Peoples R China
[3] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
[4] Univ Kent, KBS, Canterbury CT2 7NF, Kent, England
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2014年 / 6卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Optimal control; linear parabolic integro-differential equations; optimality conditions; finite element methods; a priori error estimate; INTEGRAL-EQUATIONS; DISCRETIZATION;
D O I：
10.4208/aamm.2012.m30
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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 H-1 and L-2 norms. Furthermore some numerical tests are presented to verify the theoretical results.
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页码：552 / 569
页数：18
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