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Adaptive Finite Element Methods for PDE-Constrained Optimal Control Problems

In: Reactive Flows, Diffusion and Transport

Author

Listed:
  • R. Becker

    (Université de Pau et des Pays de l’Adour, Laboratoire de Mathématiques Appliquées)

  • M. Braack

    (Universität Heidelberg, Institut für Angewandte Mathematik)

  • D. Meidner

    (Universität Heidelberg, Institut für Angewandte Mathematik)

  • R. Rannacher

    (Universität Heidelberg, Institut für Angewandte Mathematik)

  • B. Vexler

    (Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics)

Abstract

Summary We present a systematic approach to error control and mesh adaptation in the numerical solution of optimal control problems governed by partial differential equations. By the Lagrangian formalism the optimization problem is reformulated as a saddle-point boundary value problem which is discretized by a finite element Galerkin method. The accuracy of the discretization is controlled by residual-based a posteriori error estimates. The main features of this method are illustrated by examples from optimal control of heat transfer, fluid flow and parameter estimation. The contents of this article is as follows: Preliminary thoughts A general framework for a posteriori error estimation Solution process and mesh adaptation Examples of optimal control problems Conclusion and outlook References

Suggested Citation

  • R. Becker & M. Braack & D. Meidner & R. Rannacher & B. Vexler, 2007. "Adaptive Finite Element Methods for PDE-Constrained Optimal Control Problems," Springer Books, in: Willi Jäger & Rolf Rannacher & Jürgen Warnatz (ed.), Reactive Flows, Diffusion and Transport, pages 177-205, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-28396-6_8
    DOI: 10.1007/978-3-540-28396-6_8
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