Computational Optimization and Applications

, Volume 57, Issue 1, pp 205–240 | Cite as

Third order convergent time discretization for parabolic optimal control problems with control constraints

Article

Abstract

We consider a priori error analysis for a discretization of a linear quadratic parabolic optimal control problem with box constraints on the time-dependent control variable. For such problems one can show that a time-discrete solution with second order convergence can be obtained by a first order discontinuous Galerkin time discretization for the state variable and either the variational discretization approach or a post-processing strategy for the control variable. Here, by combining the two approaches for the control variable, we demonstrate that almost third order convergence with respect to the size of the time steps can be achieved.

Keywords

Optimal control Heat equation Control constraints Discontinuous Galerkin time stepping Error estimates Post-processing Variational control discretization 

Notes

Acknowledgements

The first author gratefully acknowledges financial support from the Munich Centre of Advanced Computing and the International Graduate School of Science and Engineering at the Technische Universität München. Furthermore, we would like to thank Konstantin Pieper for his help with the implementation of variational control discretization, Dominik Meidner for his helpful comments, and the anonymous referee for improving the estimate given in Lemma 6.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Lehrstuhl für Optimale Steuerung, Fakultät für MathematikTechnische Universität MünchenGarching b. MünchenGermany

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