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Computational Optimization and Applications

, Volume 46, Issue 3, pp 511–533 | Cite as

Adaptive finite element methods for mixed control-state constrained optimal control problems for elliptic boundary value problems

  • R. H. W. Hoppe
  • M. Kieweg
Article

Abstract

Mixed control-state constraints are used as a relaxation of originally state constrained optimal control problems for partial differential equations to avoid the intrinsic difficulties arising from measure-valued multipliers in the case of pure state constraints. In particular, numerical solution techniques known from the pure control constrained case such as active set strategies and interior-point methods can be used in an appropriately modified way. However, the residual-type a posteriori error estimators developed for the pure control constrained case can not be applied directly. It is the essence of this paper to show that instead one has to resort to that type of estimators known from the pure state constrained case. Up to data oscillations and consistency error terms, they provide efficient and reliable estimates for the discretization errors in the state, a regularized adjoint state, and the control. A documentation of numerical results is given to illustrate the performance of the estimators.

Keywords

Distributed optimal control problems Mixed control-state constraints Adaptive finite elements Posteriori error analysis 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Institute of MathematicsUniversity of AugsburgAugsburgGermany

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