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Inégalites d'observabilité et résolution adaptative de l'équation de Vlasov par éléments finis hiérarchiques

Michel Mehrenberger 1, 2
2 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : The first part deals with the study of observability inequalities which appear in control theory. We give an abstract theorem which
enables to deduce the observability of a system by compact perturbation, with a weakened condition on the perturbed operator. This theorem is then applied to the observability of some weakened coupled systems. We also prove the optimality of a recent theorem
concerning a generalisation of the Parseval identity to the divided differences of exponentials. The second part of this work deals
with the numerical resolution of the Vlasov equation by using semi-lagrangian type schemes. We first prove the convergence of arbitrarily high order schemes, by completing former results. We the develop a new numerical method based on biquadratic hierarchical finite elements, which enables here an efficient parallelisation. In the case of a piecewise affine reconstruction, we define a refinement strategy and quantities which control the error produced at each time step, in order to construct at last an adaptive algorithm, of which we prove the convergence.
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https://tel.archives-ouvertes.fr/tel-00008254
Contributor : Michel Mehrenberger <>
Submitted on : Tuesday, February 1, 2005 - 11:26:49 AM
Last modification on : Tuesday, March 2, 2021 - 5:12:04 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:04:37 PM

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  • HAL Id : tel-00008254, version 1

Citation

Michel Mehrenberger. Inégalites d'observabilité et résolution adaptative de l'équation de Vlasov par éléments finis hiérarchiques. Informatique [cs]. Université Louis Pasteur - Strasbourg I, 2004. Français. ⟨NNT : 2004STR13124⟩. ⟨tel-00008254⟩

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