A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems
A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems
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DOI：
10.4208/aamm.2012.m30
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发表时间：
2014-10
影响因子：
1.4
通讯作者：
W. Shen;L. Ge;Danping Yang;Wenbin Liu
中科院分区：
文献类型：
--
作者：
W. Shen;L. Ge;Danping Yang;Wenbin Liu
在本文中，我们研究了由线性抛物型积分微分方程控制的最优控制问题的数学公式，并提出了最优性条件。然后我们建立了它的弱公式和有限元近似方案。在此基础上，我们推导了 H 1 和 L 2 范数中有限元近似的先验误差估计。此外，还进行了一些数值试验来验证理论结果。
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.