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

Patrick Joly 1 Sébastien Tordeux 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness $\epsilon$ is small with respect to the wavelength. In Part I [P. Joly and S. Tordeux, Multiscale Model. Simul. 5 (2006), no. 1, 304--336 (electronic); MR2221320 (2007e:35041)], we derived formally an asymptotic expansion of the solution with respect to $\epsilon$ 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.
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Patrick Joly, Sébastien Tordeux. Matching of asymptotic expansions for waves propagation in media with thin slots. II. The error estimates. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2008, 42 (2), pp.193--221. ⟨10.1051/m2an:2008004⟩. ⟨inria-00527445⟩

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