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A-Priori Error Bounds for Finite Element Approximation of Elliptic Optimal Control Problems with Gradient Constraints

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Trends in PDE Constrained Optimization

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 165))

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Abstract

The finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state is considered. We review recent results on the error analysis for various discretization approaches and prove a new bound for the problem without control constraints.

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Acknowledgements

The authors acknowledge support of the DFG priority program 1253 through grants DFG HI689/5-1 and DFG DE611/4-2.

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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 & Michael Hinze

Authors
  1. Klaus Deckelnick
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  2. Michael Hinze
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Corresponding author

Correspondence to Michael Hinze .

Editor information

Editors and Affiliations

  1. Department Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

    Günter Leugering

  2. Institut für Dynamik komplexer technisch, Max-Planck-Institut, Magdeburg, Germany

    Peter Benner

  3. Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Dortmund, Germany

    Sebastian Engell

  4. Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany

    Andreas Griewank

  5. Mathematisches Institut, Universität Basel, Basel, Switzerland

    Helmut Harbrecht

  6. Fachbereich Mathematik Optimierung und Approximation, Universität Hamburg, Hamburg, Germany

    Michael Hinze

  7. Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

    Rolf Rannacher

  8. Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

    Stefan Ulbrich

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Deckelnick, K., Hinze, M. (2014). A-Priori Error Bounds for Finite Element Approximation of Elliptic Optimal Control Problems with Gradient Constraints. In: Leugering, G., et al. Trends in PDE Constrained Optimization. International Series of Numerical Mathematics, vol 165. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-05083-6_23

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