Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation
Lissy, Pierre; Roventa, Ionel (2016), Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation. https://basepub.dauphine.fr/handle/123456789/17174
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-01338619
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Department of Mathematics [UCV]
Abstract (EN)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.
Subjects / Keywordswave equation; control approximation; moment problem; biorthogonal families
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