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A-posteriori error estimates for optimal control problems with state and control constraints

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Abstract

We discuss the full discretization of an elliptic optimal control problem with pointwise control and state constraints. We provide the first reliable a-posteriori error estimator that contains only computable quantities for this class of problems. Moreover, we show, that the error estimator converges to zero if one has convergence of the discrete solutions to the solution of the original problem. The theory is illustrated by numerical tests.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Duisburg-Essen, Forsthausweg 2, 47057, Duisburg, Germany

    Arnd Rösch

  2. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, 4040, Linz, Austria

    Daniel Wachsmuth

Authors
  1. Arnd Rösch
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  2. Daniel Wachsmuth
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Correspondence to Daniel Wachsmuth.

Additional information

Daniel Wachsmuth was partially supported by FWF project P21564.

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Rösch, A., Wachsmuth, D. A-posteriori error estimates for optimal control problems with state and control constraints. Numer. Math. 120, 733–762 (2012). https://doi.org/10.1007/s00211-011-0422-z

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  • DOI: https://doi.org/10.1007/s00211-011-0422-z

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