A Characteristic Finite Element Method for Constrained Convection-Diffusion-Reaction Optimal Control Problems

A Characteristic Finite Element Method for Constrained Convection-Diffusion-Reaction Optimal Control Problems

Year:    2013

Journal of Computational Mathematics, Vol. 31 (2013), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1210-m3966

Journal of Computational Mathematics, Vol. 31 (2013), Iss. 1 : pp. 88–106

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

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