Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 217493, 21 pages
http://dx.doi.org/10.1155/2011/217493
Research Article

Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems

Zuliang Lu1,2

1School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404000, China
2College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, China

Received 12 May 2011; Accepted 30 June 2011

Academic Editor: Kue-Hong Chen

Copyright © 2011 Zuliang Lu. 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

We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element method for the optimal control problems. Next we introduce an adaptive algorithm to guide the mesh refinement. A numerical example is given to demonstrate our theoretical results.