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

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  • Andreas Springer
  • Boris Vexler

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Andreas Springer & Boris Vexler, 2014. "Third order convergent time discretization for parabolic optimal control problems with control constraints," Computational Optimization and Applications, Springer, vol. 57(1), pages 205-240, January.
    • Handle: RePEc:spr:coopap:v:57:y:2014:i:1:p:205-240
    DOI: 10.1007/s10589-013-9580-5
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    Cited by:

    1. Konstantinos Chrysafinos & Efthimios Karatzas, 2015. "Symmetric error estimates for discontinuous Galerkin time-stepping schemes for optimal control problems constrained to evolutionary Stokes equations," Computational Optimization and Applications, Springer, vol. 60(3), pages 719-751, April.

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