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Semidiscretization and error estimates for distributed control of the instationary Navier-Stokes equations

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Summary.

Optimal control problems governed by the two-dimensional instationary Navier–Stokes equations and their spatial discretizations with finite elements are investigated. A concept of semi–discrete solutions to the control problem is introduced which is utilized to prove existence and uniqueness of discrete controls in neighborhoods of regular continuous solutions. Furthermore, an optimal error estimate in terms of the spatial discretization parameter is given.

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Authors and Affiliations

  1. Institut für Analysis und Numerik, Otto–von–Guericke–Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Klaus Deckelnick

  2. Fakultät für Mathematik, Institut für Numerische Mathematik, Technische Universität Dresden, 01062, Dresden, Germany

    Michael Hinze

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  1. Klaus Deckelnick
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  2. Michael Hinze
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Correspondence to Klaus Deckelnick.

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Correspondence to: M. Hinze

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Deckelnick, K., Hinze, M. Semidiscretization and error estimates for distributed control of the instationary Navier-Stokes equations. Numer. Math. 97, 297–320 (2004). https://doi.org/10.1007/s00211-003-0507-4

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  • DOI: https://doi.org/10.1007/s00211-003-0507-4

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