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

Patrick Joly; Sébastien Tordeux

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 2, page 193-221
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Joly, Patrick, and Tordeux, Sébastien. "Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates." ESAIM: Mathematical Modelling and Numerical Analysis 42.2 (2008): 193-221. <http://eudml.org/doc/250430>.

@article{Joly2008,
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. },
author = {Joly, Patrick, Tordeux, Sébastien},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Slit; slot; wave equation; Helmholtz equation; approximate model; matching of asymptotic expansions.; slit; matching of asymptotic expansions},
language = {eng},
month = {3},
number = {2},
pages = {193-221},
publisher = {EDP Sciences},
title = {Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates},
url = {http://eudml.org/doc/250430},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Joly, Patrick
AU - Tordeux, Sébastien
TI - Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/3//
PB - EDP Sciences
VL - 42
IS - 2
SP - 193
EP - 221
AB - 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.
LA - eng
KW - Slit; slot; wave equation; Helmholtz equation; approximate model; matching of asymptotic expansions.; slit; matching of asymptotic expansions
UR - http://eudml.org/doc/250430
ER -

References

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