Computing

, Volume 84, Issue 1–2, pp 27–48 | Cite as

Implementation and analysis of multigrid schemes with finite elements for elliptic optimal control problems

Article

Abstract

The detailed implementation and analysis of a finite element multigrid scheme for the solution of elliptic optimal control problems is presented. A particular focus is in the definition of smoothing strategies for the case of constrained control problems. For this setting, convergence of the multigrid scheme is discussed based on the BPX framework. Results of numerical experiments are reported to illustrate and validate the optimal efficiency and robustness of the performance of the present multigrid strategy.

Keywords

Elliptic optimal control problem Finite elements Multigrid method 

Mathematics Subject Classification (2000)

49K20 65N12 65N30 65N55 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • O. Lass
    • 1
  • M. Vallejos
    • 1
    • 2
  • A. Borzi
    • 1
    • 3
  • C. C. Douglas
    • 4
  1. 1.Institut für Mathematik und Wissenschaftliches RechnenKarl-Franzens-UniversitätGrazAustria
  2. 2.Institute of Mathematics, College of ScienceUniversity of the PhilippinesDilimanPhilippines
  3. 3.Dipartimento e Facoltà di IngegneriaUniversità degli Studi del SannioBeneventoItaly
  4. 4.Mathematics DepartmentUniversity of WyomingLaramieUSA

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