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Theses

Problèmes faiblement bien posés : discrétisation et applications.

Abstract : In this thesis we consider the numerical approximation of weakly well-posed problems by finite difference schemes. We define new concepts which take into account the loss of regularity coming from the weak well-posedness, and we extend the Lax-Richtmyer theorem. Using perturbation theory and Puiseux expansion, we compute the convergence factor of the classical schemes. We give numerical evidences for our results. In a second part we are interested in a special class of weakly well-posed problems: the perfectly matched layers designed by Berenger. We give new energy estimates for the Maxwell system and the associated Yee scheme. We finally study the asymptotic behavior in time of the model using geometric optics.
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https://tel.archives-ouvertes.fr/tel-00545794
Contributor : Laurence Halpern <>
Submitted on : Sunday, December 12, 2010 - 8:00:45 PM
Last modification on : Tuesday, October 20, 2020 - 3:56:34 PM
Long-term archiving on: : Friday, December 2, 2016 - 5:00:38 PM

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  • HAL Id : tel-00545794, version 1

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Sabrina Petit-Bergez. Problèmes faiblement bien posés : discrétisation et applications.. Mathématiques [math]. Université Paris-Nord - Paris XIII, 2006. Français. ⟨tel-00545794⟩

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