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.

引用

页码：552 / 569

页数：18

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