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Volume 31, Issue 1
A Characteristic Finite Element Method for Constrained Convection-Diffusion-Reaction Optimal Control Problems

Hongfei Fu, Hongxing Rui & Hui Guo

DOI: 10.4208/jcm.1210-m3966

J. Comp. Math., 31 (2013), pp. 88-106.

Published online: 2013-02

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  • Abstract

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  $L^2$-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.

  • Keywords

Characteristic finite element method, Constrained optimal control, Convection-diffusion-reaction equations, Pointwise inequality constraints, A priori error estimates.

  • AMS Subject Headings

49J20, 65M15, 65M25, 65M60.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-31-88, author = {Hongfei Fu, Hongxing Rui and Hui Guo}, title = {A Characteristic Finite Element Method for Constrained Convection-Diffusion-Reaction Optimal Control Problems}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {1}, pages = {88--106}, abstract = {

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  $L^2$-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1210-m3966}, url = {http://global-sci.org/intro/article_detail/jcm/9723.html} }
TY - JOUR T1 - A Characteristic Finite Element Method for Constrained Convection-Diffusion-Reaction Optimal Control Problems AU - Hongfei Fu, Hongxing Rui & Hui Guo JO - Journal of Computational Mathematics VL - 1 SP - 88 EP - 106 PY - 2013 DA - 2013/02 SN - 31 DO - http://doi.org/10.4208/jcm.1210-m3966 UR - https://global-sci.org/intro/article_detail/jcm/9723.html KW - Characteristic finite element method, Constrained optimal control, Convection-diffusion-reaction equations, Pointwise inequality constraints, A priori error estimates. AB -

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  $L^2$-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.

Hongfei Fu, Hongxing Rui and Hui Guo. (2013). A Characteristic Finite Element Method for Constrained Convection-Diffusion-Reaction Optimal Control Problems. Journal of Computational Mathematics. 31 (1). 88-106. doi:10.4208/jcm.1210-m3966
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