Analyse asymptotique multi-échelle et conditions aux limites approchées pour un problème de couche mince dans un domaine à coin

Abstract : This work consists in the asymptotic analysis of a transmission problem with thin layer in a two-dimensional corner domain. An asymptotic expansion of the solution with respect to the thickness of the layer is constructed. Due to the corner, singularities appear which prevent from constructing the expansion through an alternative resolution between the interior domain and the layer. The singularities are handled with the help of profiles constructed in an infinite domain with layer of thickness 1 via the Mellin transform.\par Next, the efficiency of the approximate boundary condition (obtained for smooth domains) is studied. We show that the performance deteriorates for corner domains, especially when the opening of the corner is large. Numerical tests are given, which confirm the theoretical results.
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Submitted on : Friday, February 27, 2004 - 9:57:21 AM
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Grégory Vial. Analyse asymptotique multi-échelle et conditions aux limites approchées pour un problème de couche mince dans un domaine à coin. Mathématiques [math]. Université Rennes 1, 2003. Français. ⟨tel-00005153⟩

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