Influence of a rough thin layer on the steady-state potential

In this paper, we study the behavior of the steady-state voltage potentials in a material composed by an interior medium surrounded by a rough thin layer and embedded in an ambient bounded medium. The roughness of the layer is supposed to be ε–periodic, ε being the small thickness of the layer. We present and validate numerically the rigorous approximate transmissions proved by Ciuperca et al. in [1]. This paper extends previous works in which the layer had a constant thickness. Key-words: Asymptotic analysis, Finite Element Method, Laplace equations ∗ Université de Lyon, Université Lyon 1, CNRS, UMR 5208, Institut Camille Jordan, Bat. Braconnier, 43 boulevard du 11 novembre 1918, F 69622 Villeurbanne Cedex, France † Laboratoire Ampère UMR CNRS 5005, Universit de Lyon, École Centrale de Lyon, F-69134 Écully, France ‡ INRIA Bordeaux-Sud-Ouest, Institut de Mathématiques de Bordeaux, CNRS UMR 5251 & Université de Bordeaux1, 351 cours de la Libération, 33405 Talence Cedex, France in ria -0 03 84 19 8, v er si on 2 6 Au g 20 09 Influence d’une couche rugueuse sur le potentiel électrique Résumé : Mots-clés : Analyse Asymptotique, Méthode des Eléments Finis, Equations de Laplace in ria -0 03 84 19 8, v er si on 2 6 Au g 20 09 Approximate transmission conditions for a rough thin layer 3