Geodesic
Matching of asymptotic expansions for waves propagation in media with thin slots II : the error estimates
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 2, pp. 193-221

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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.

DOI : 10.1051/m2an:2008004
Classification : 35J05, 34E05, 78A45, 78A50
Keywords: slit, slot, wave equation, Helmholtz equation, approximate model, matching of asymptotic expansions 
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     author = {Joly, Patrick and Tordeux, S\'ebastien},
     title = {Matching of asymptotic expansions for waves propagation in media with thin slots {II} : the error estimates},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {193--221},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {2},
     year = {2008},
     doi = {10.1051/m2an:2008004},
     mrnumber = {2405145},
     zbl = {1132.35348},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008004/}
}
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Joly, Patrick; Tordeux, Sébastien. Matching of asymptotic expansions for waves propagation in media with thin slots II : the error estimates. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 2, pp. 193-221. doi: 10.1051/m2an:2008004

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