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Error estimates for the discretization of elliptic control problems with pointwise control and state constraints

  • S. Cherednichenko
  • A. Rösch
Article

Abstract

A family of elliptic optimal control problems with pointwise constraints on control and state is considered. We are interested in approximation of the optimal solution by a finite element discretization of the involved partial differential equations. The discretization error for a problem with mixed state constraints is estimated in the semidiscrete case and in the fully discrete scheme with the convergence of order h|ln h| and h 1/2, respectively. However, considering the unregularized continuous problem and the discrete regularized version, and choosing suitable relation between the regularization parameter and the mesh size, i.e., εh 2, a convergence order arbitrary close to 1, i.e., h 1−β is obtained. Therefore, we benefit from tuning the involved parameters.

Keywords

Elliptic optimal control problems State constraints Discrete approximations Error estimates Mixed control-state constraints 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversity Duisburg-EssenDuisburgGermany

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