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Convergence of Adaptive Finite Elements for Optimal Control Problems with Control Constraints

  • Kristina Kohls
  • Kunibert G. SiebertEmail author
  • Arnd Rösch
Chapter
Part of the International Series of Numerical Mathematics book series (ISNM, volume 165)

Abstract

We summarize our findings in the analysis of adaptive finite element methods for the efficient discretization of control constrained optimal control problems. We particularly focus on convergence of the adaptive method, i.e., we show that the sequence of adaptively generated discrete solutions converges to the true solution. We restrict the presentation to a simple model problem to highlight the key components of the convergence proof and comment on generalizations of the presented result.

Keywords

Adaptive finite elements Aposteriori error estimators Convergence analysis Optimal control Control constraints 

Mathematics Subject Classification (2010)

65N30 65N12 49J20 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Kristina Kohls
    • 1
  • Kunibert G. Siebert
    • 1
    Email author
  • Arnd Rösch
    • 2
  1. 1.Institut für Angewandte Analysis und Numerische Simulation, Fachbereich MathematikUniversität StuttgartStuttgartGermany
  2. 2.Fakultät für MathematikEssenGermany

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