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.