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

W. Alt (), N. Bräutigam () and D. Karolewski
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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

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 745-752 from Springer

Abstract: 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.

Keywords: Control Problem; Optimal Control Problem; Collocation Method; Element Approximation; Discrete Control (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-69777-0_89

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