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Reliable a posteriori error estimation for state-constrained optimal control

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Abstract

We derive a reliable a posteriori error estimator for a state-constrained elliptic optimal control problem taking into account both regularisation and discretisation. The estimator is applicable to finite element discretisations of the problem with both discretised and non-discretised control. The performance of our estimator is illustrated by several numerical examples for which we also introduce an adaptation strategy for the regularisation parameter.

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Authors and Affiliations

  1. Universität Duisburg-Essen, Thea-Leymann-Str. 9, 45127, Essen, Germany

    A. Rösch

  2. Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    K. G. Siebert

  3. TU Dortmund, Faculty of Mathematics, LS X, Vogelpothsweg 87, 44227, Dortmund, Germany

    S. Steinig

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  1. A. Rösch
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  2. K. G. Siebert
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Rösch, A., Siebert, K.G. & Steinig, S. Reliable a posteriori error estimation for state-constrained optimal control. Comput Optim Appl 68, 121–162 (2017). https://doi.org/10.1007/s10589-017-9908-7

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