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A Collocation Method for Quadratic Control Problems Governed by Ordinary Elliptic Differential Equations

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • W. Alt

    (Friedrich-Schiller-Universität Jena, Institut für Angewandte Mathematik)

  • N. Bräutigam

    (Friedrich-Alexander-Universität Erlangen-Nürnberg, Institut für Angewandte Mathematik)

  • D. Karolewski

    (Friedrich-Schiller-Universität Jena, Institut für Angewandte Mathematik)

Abstract

We investigate discretizations for a class of quadratic optimal control problems governed by one-dimensional elliptic differential equations. In contrast to the papers [3] dealing with finite element approximations and [2, 1] dealing with finite difference approximation, the dicretizations considered here are based on a collocation method using quadratic splines for the state equation. Under the assumption that the optimal control has bounded variation we prove discrete and continuous quadratic convergence of approximating controls.

Suggested Citation

  • W. Alt & N. Bräutigam & D. Karolewski, 2008. "A Collocation Method for Quadratic Control Problems Governed by Ordinary Elliptic Differential Equations," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 745-752, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_89
    DOI: 10.1007/978-3-540-69777-0_89
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