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Computational Optimization and Applications

, Volume 62, Issue 1, pp 31–65 | Cite as

Boundary concentrated finite elements for optimal control problems with distributed observation

  • S. Beuchler
  • K. Hofer
  • D. Wachsmuth
  • J.-E. Wurst
Article

Abstract

We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. If the constraint is a \(H^{1+\delta }(\Omega )\) regular elliptic PDE with smooth differential operator and source term, we prove for the two dimensional case that the discretization error in the \(L_2\) norm decreases like \(N^{-\delta }\), where \(N\) is the number of unknowns. Our approach is suitable for solving a wide class of problems, among them piecewise defined data and tracking functionals acting only on a subdomain of \(\Omega \). We present several numerical results.

Keywords

Optimal control Elliptic partial differential equation Higher-order discretization Boundary-concentrated finite elements A priori error estimates 

Notes

Acknowledgments

This work was funded by the Austrian Science Fund (FWF) Grant P23484-N18.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • S. Beuchler
    • 1
  • K. Hofer
    • 1
  • D. Wachsmuth
    • 2
  • J.-E. Wurst
    • 2
  1. 1.Institut für Numerische SimulationUniversität BonnBonnGermany
  2. 2.Institut für MathematikUniversität WürzburgWürzburgGermany

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