Computational Optimization and Applications

, Volume 60, Issue 3, pp 719–751 | Cite as

Symmetric error estimates for discontinuous Galerkin time-stepping schemes for optimal control problems constrained to evolutionary Stokes equations

  • Konstantinos Chrysafinos
  • Efthimios N. Karatzas
Article

Abstract

We consider fully discrete finite element approximations of a distributed optimal control problem, constrained by the evolutionary Stokes equations. Conforming finite element methods for spatial discretization combined with discontinuous time-stepping Galerkin schemes are being used for the space-time discretization. Error estimates are proved under weak regularity hypotheses for the state, adjoint and control variables. The estimates are also applicable when high order schemes are being used. Computational examples validating our expected rates of convergence are also provided.

Keywords

Discontinuous time-stepping schemes Finite element approximations Stokes equations Velocity tracking problem  Distributed controls Error estimates 

Mathematics Subject Classification

65M60 49J20 

Notes

Acknowledgments

Efthimios N. Karatzas is supported by Papakyriakopoulos Scholarship.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Konstantinos Chrysafinos
    • 1
  • Efthimios N. Karatzas
    • 1
  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece

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