Calcolo

, Volume 44, Issue 3, pp 137–158

Optimal control in non-convex domains: a priori discretization error estimates

  • Thomas Apel
  • Arnd Rösch
  • Gunter Winkler
Article

DOI: 10.1007/s10092-007-0133-0

Cite this article as:
Apel, T., Rösch, A. & Winkler, G. Calcolo (2007) 44: 137. doi:10.1007/s10092-007-0133-0

Abstract

An optimal control problem for a two-dimensional elliptic equation 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. Approximations of the optimal solution of the continuous optimal control problem are constructed by a projection of the discrete adjoint state. It is proved that these approximations have convergence order h2.

Keywords Linear-quadratic optimal control problems, error estimates, elliptic equations, non-convex domains, corner singularities, control constraints, superconvergence.

Mathematics Subject Classification (2000): 49K20, 49M25, 65N30, 65N50

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Thomas Apel
    • 1
  • Arnd Rösch
    • 2
  • Gunter Winkler
    • 1
  1. 1.Institut für Mathematik und Bauinformatik, Fakultät für Bauingenieur- und Vermessungswesen, Universität der Bundeswehr München, 85577 NeubibergGermany
  2. 2.A. Rösch Fachbereich Mathematik, Universität Duisburg-Essen, Forsthausweg 2, 47057 DuisburgGermany