Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 579047, 12 pages
http://dx.doi.org/10.1155/2014/579047
Research Article

Superconvergence for General Convex Optimal Control Problems Governed by Semilinear Parabolic Equations

1Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, China
2School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631, China

Received 16 September 2013; Accepted 12 December 2013; Published 10 February 2014

Academic Editors: M. Braack, Y. M. Cheng, and W. Yeih

Copyright © 2014 Yongquan Dai and Yanping Chen. 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 superconvergence for the semidiscrete finite element approximation of distributed convex optimal control problems governed by semilinear parabolic equations. The state and costate are approximated by the piecewise linear functions and the control is approximated by piecewise constant functions. We present the superconvergence analysis for both the control variable and the state variables.