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Convergence of Adaptive Finite Elements for Optimal Control Problems with Control Constraints

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Trends in PDE Constrained Optimization

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

Abstract

We summarize our findings in the analysis of adaptive finite element methods for the efficient discretization of control constrained optimal control problems. We particularly focus on convergence of the adaptive method, i.e., we show that the sequence of adaptively generated discrete solutions converges to the true solution. We restrict the presentation to a simple model problem to highlight the key components of the convergence proof and comment on generalizations of the presented result.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Analysis und Numerische Simulation, Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany

    Kristina Kohls & Kunibert G. Siebert

  2. Fakultät für Mathematik, Thea-Leymann-Straße 9, D-45127, Essen, Germany

    Arnd Rösch

Authors
  1. Kristina Kohls
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  2. Kunibert G. Siebert
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  3. Arnd Rösch
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Corresponding author

Correspondence to Kunibert G. Siebert .

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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Kohls, K., Siebert, K.G., Rösch, A. (2014). Convergence of Adaptive Finite Elements for Optimal Control Problems with Control 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_25

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