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Numerische Mathematik

, Volume 120, Issue 4, pp 733–762 | Cite as

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

  • Arnd Rösch
  • Daniel Wachsmuth
Article

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.

Mathematics Subject Classification (2000)

Primary 65N15 Secondary 49M25 65N30 65K10 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität Duisburg-EssenDuisburgGermany
  2. 2.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria

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