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A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems

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Constrained Optimization and Optimal Control for Partial Differential Equations

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 160))

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Abstract

In this article we summarize recent results on a priori error estimates for space-time finite element discretizations of linear-quadratic parabolic optimal control problems. We consider the following three cases: problems without inequality constraints, problems with pointwise control constraints, and problems with state constraints pointwise in time. For all cases, error estimates with respect to the temporal and to the spatial discretization parameters are derived. The results are illustrated by numerical examples.

Mathematics Subject Classification (2000). 35K20, 49J20, 49M05, 49M15, 49M25, 49M29, 49N10, 65M12, 65M15, 65M60.

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Authors and Affiliations

  1. Lehrstuhl für Mathematische Optimierung, Technische Universität München Fakultät für Mathematik, Boltzmannstraße 3, D-85748, Garching b. München, Germany

    Dominik Meidner & Boris Vexler

Authors
  1. Dominik Meidner
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  2. Boris Vexler
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Corresponding author

Correspondence to Dominik Meidner .

Editor information

Editors and Affiliations

  1. , Department Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, Erlangen, 91058, Germany

    Günter Leugering

  2. , Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Geschossbau 2, Dortmund, 44221, Germany

    Sebastian Engell

  3. , Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, Berlin, 12489, Germany

    Andreas Griewank

  4. , Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Michael Hinze

  5. , Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 293, Heidelberg, 69120, Germany

    Rolf Rannacher

  6. , FB 4 - Department Mathematik, Universität Trier, Trier, 54286, Germany

    Volker Schulz

  7. Fakultät für Mathematik, M1, Lehrstuhl für Mathematische Optimierung, Technische Universität München, Boltzmannstr. 3, Garching bei München, 85748, Germany

    Michael Ulbrich

  8. , Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostrasse 15, Darmstadt, 64293, Germany

    Stefan Ulbrich

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Meidner, D., Vexler, B. (2012). A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems. In: Leugering, G., et al. Constrained Optimization and Optimal Control for Partial Differential Equations. International Series of Numerical Mathematics, vol 160. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0133-1_23

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