Discretization Error Estimates for an Optimal Control Problem in a Nonconvex Domain

  • Th. Apel
  • A. Rösch
  • G. Winkler

Abstract

An optimal control problem for a 2-d elliptic equation and with pointwise control constraints is investigated. The domain is assumed to be polygonal but non-convex. The corner singularities are treated by a priori mesh grading. A second order approximation of the optimal control is constructed by a projection of the discrete adjoint state. Here we summarize the results from [1] and add further numerical tests.

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References

  1. 1.
    Apel, T., Rösch, A., Winkler, G.: Optimal control in nonconvex domains. RICAM Report, 17 (2005-17). http://www.ricam.oeaw.ac.at/publications/reports/.Google Scholar
  2. 2.
    Hinze, M.: A variational discretization concept in control constrained optimization: The linear-quadratic case. Computational Optimization and Applications, 30 45–63 (2005)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Meyer, C., Rösch, A.: Superconvergence properties of optimal control problems. SIAM J. Control and Optimization, 43 970–985 (2004)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Th. Apel
    • 1
  • A. Rösch
    • 2
  • G. Winkler
    • 1
  1. 1.Institut für Mathematik und Bauinformatik, Fakultät für Bauingenieur- und VermessungswesenUniversität der Bundeswehr MünchenNeubibergGermany
  2. 2.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria

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