A CHARACTERISTIC FINITE ELEMENT METHOD FOR CONSTRAINED CONVECTION-DIFFUSION-REACTION OPTIMAL CONTROL PROBLEMS

In this paper, we develop a priori error estimates for the solution of constrained convection-diffusion-reaction optimal control problems using a characteristic finite element method. The cost functional of the optimal control problems consists of three parts： The first part is about integration of...

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Bibliographic Details
Published in:Journal of computational mathematics 2013, Vol.31 (1), p.88-106
Main Authors: Fu, Hongfei, Rui, Hongxing, Guo, Hui
Format: Article
Language:English
Subjects:
使用特性
先验误差估计
对流
扩散反应
最优控制问题
有限元方法
特征约束
离散状态
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Summary:In this paper, we develop a priori error estimates for the solution of constrained convection-diffusion-reaction optimal control problems using a characteristic finite element method. The cost functional of the optimal control problems consists of three parts： The first part is about integration of the state over the whole time interval, the second part refers to final-time state, and the third part is a regularization term about the control. We discretize the state and co-state by piecewise linear continuous functions, while the control is approximated by piecewise constant functions. Pointwise inequality function constraints on the control are considered, and optimal a L2-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.
ISSN:0254-9409
1991-7139
DOI:10.4208/jcm.1210-m3966