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Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates

Published online by Cambridge University Press:  27 March 2008

Patrick Joly  and
Sébastien Tordeux
Patrick Joly
Affiliation:
Projet POEMS, Bâtiment 13, INRIA, Domaine de Voluceau - Rocquencourt - B.P. 105, 78153 Le Chesnay Cedex, France. patrick.joly@inria.fr
Sébastien Tordeux
Affiliation:
Institut de Mathématiques de Toulouse, Université de Toulouse, 135 avenue de Rangueil, 31077 Toulouse Cedex 4, France. sebastien.tordeux@insa-toulouse.fr
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Abstract

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.

Keywords

Slitslotwave equationHelmholtz equationapproximate modelmatching of asymptotic expansions.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 2 , March 2008 , pp. 193 - 221
Copyright
© EDP Sciences, SMAI, 2008

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