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Reliable a posteriori error estimation for state-constrained optimal control

Author

Listed:
  • A. Rösch

    (Universität Duisburg-Essen)

  • K. G. Siebert

    (Universität Stuttgart)

  • S. Steinig

    () (Faculty of Mathematics)

Abstract

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.

Suggested Citation

  • A. Rösch & K. G. Siebert & S. Steinig, 2017. "Reliable a posteriori error estimation for state-constrained optimal control," Computational Optimization and Applications, Springer, vol. 68(1), pages 121-162, September.
  • Handle: RePEc:spr:coopap:v:68:y:2017:i:1:d:10.1007_s10589-017-9908-7
    DOI: 10.1007/s10589-017-9908-7
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    References listed on IDEAS

    as
    1. M. Hinze & C. Meyer, 2010. "Variational discretization of Lavrentiev-regularized state constrained elliptic optimal control problems," Computational Optimization and Applications, Springer, vol. 46(3), pages 487-510, July.
    2. R. Hoppe & M. Kieweg, 2010. "Adaptive finite element methods for mixed control-state constrained optimal control problems for elliptic boundary value problems," Computational Optimization and Applications, Springer, vol. 46(3), pages 511-533, July.
    3. Michael Hinze & Anton Schiela, 2011. "Discretization of interior point methods for state constrained elliptic optimal control problems: optimal error estimates and parameter adjustment," Computational Optimization and Applications, Springer, vol. 48(3), pages 581-600, April.
    4. Olaf Benedix & Boris Vexler, 2009. "A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints," Computational Optimization and Applications, Springer, vol. 44(1), pages 3-25, October.
    5. W. Wollner, 2010. "A posteriori error estimates for a finite element discretization of interior point methods for an elliptic optimization problem with state constraints," Computational Optimization and Applications, Springer, vol. 47(1), pages 133-159, September.
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