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

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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.

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Acknowledgments

Efthimios N. Karatzas is supported by Papakyriakopoulos Scholarship.

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  1. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

    Konstantinos Chrysafinos & Efthimios N. Karatzas

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  1. Konstantinos Chrysafinos
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  2. Efthimios N. Karatzas
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Correspondence to Konstantinos Chrysafinos.

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Chrysafinos, K., Karatzas, E.N. Symmetric error estimates for discontinuous Galerkin time-stepping schemes for optimal control problems constrained to evolutionary Stokes equations. Comput Optim Appl 60, 719–751 (2015). https://doi.org/10.1007/s10589-014-9695-3

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