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

Konstantinos Chrysafinos () and Efthimios Karatzas ()

Computational Optimization and Applications, 2015, vol. 60, issue 3, 719-751

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. Copyright Springer Science+Business Media New York 2015

Keywords: Discontinuous time-stepping schemes; Finite element approximations; Stokes equations; Velocity tracking problem; Distributed controls; Error estimates; 65M60; 49J20 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10589-014-9695-3

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