Volume 42, Number 2, March-April 2008
|Page(s)||193 - 221|
|Published online||27 March 2008|
Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates
Projet POEMS, Bâtiment 13, INRIA, Domaine de Voluceau - Rocquencourt - B.P. 105, 78153 Le Chesnay Cedex, France. firstname.lastname@example.org
2 Institut de Mathématiques de Toulouse, Université de Toulouse, 135 avenue de Rangueil, 31077 Toulouse Cedex 4, France. email@example.com
Revised: 20 September 2007
We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between the exact solutions and truncated expansions at any order.
Mathematics Subject Classification: 35J05 / 34E05 / 78A45 / 78A50
Key words: Slit / slot / wave equation / Helmholtz equation / approximate model / matching of asymptotic expansions.
© EDP Sciences, SMAI, 2008
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