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Numerische Mathematik

, Volume 118, Issue 3, pp 587–600 | Cite as

A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state

  • C. Ortner
  • W. WollnerEmail author
Article

Abstract

We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly from classical results for the W 1,∞-error of the finite element projection, without using adjoint information. If the control space is discretized directly, we first prove a regularity result for the optimal control to control the approximation error, based on which we then obtain analogous convergence rates.

Mathematics Subject Classification (2000)

65K10 65N30 49K20 49M25 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.Institut für Angewandte MathematikRuprecht-Karls-Universität HeidelbergHeidelbergGermany

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