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Journal of Mathematics
Volume 2017, Article ID 6901467, 14 pages
https://doi.org/10.1155/2017/6901467
Research Article

A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem

College of Mathematical Sciences, Shandong Normal University, Jinan, China

Correspondence should be addressed to Zhaojie Zhou; nc.ude.unds@eijoahzuohz

Received 4 November 2016; Accepted 9 January 2017; Published 21 February 2017

Academic Editor: Ram Jiwari

Copyright © 2017 Qingjin Xu and Zhaojie Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we investigate a mixed discontinuous Galerkin approximation of time dependent convection diffusion optimal control problem with control constraints based on the combination of a mixed finite element method for the elliptic part and a discontinuous Galerkin method for the hyperbolic part of the state equation. The control variable is approximated by variational discretization approach. A priori error estimates of the state, adjoint state, and control are derived for both semidiscrete scheme and fully discrete scheme. Numerical example is given to show the effectiveness of the numerical scheme.