Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation

Pierre Lissy 1 Ionel Roventa 2
1 CEREMADE, Universit e Paris Dauphine
CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
Abstract : We consider a finite-differences semi-discrete scheme for the approximation of boundary controls for the one-dimensional wave equation. The high frequency numerical spurious oscillations lead to a loss of the uniform (with respect to the mesh-size) controllability property of the semi-discrete model in the natural setting. We prove that, by filtering the high frequencies of the initial data in an optimal range, we restore the uniform controllability property. Moreover, we obtain a relation between the range of filtration and the minimal time of control needed to ensure the uniform controllability, recovering in many cases the usual minimal time to control the (continuous) wave equation.
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https://hal.archives-ouvertes.fr/hal-01338619
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Soumis le : mardi 28 juin 2016 - 20:09:33
Dernière modification le : mercredi 28 septembre 2016 - 16:04:58
Document(s) archivé(s) le : jeudi 29 septembre 2016 - 12:10:01

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Pierre Lissy, Ionel Roventa. Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation. 2016. <hal-01338619>

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