Issue |
ESAIM: ProcS
Volume 61, 2018
43-ème Congrès National d'Analyse Numérique, CANUM2016
|
|
---|---|---|
Page(s) | 38 - 54 | |
DOI | https://doi.org/10.1051/proc/201861038 | |
Published online | 12 October 2018 |
Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★
Univ Lyon, École centrale de Lyon, CNRS UMR 5208, Institut Camille Jordan, 36 avenue Guy de Collongue, Écully Cedex, F-69134, France
Problems involving materials with thin layers arise in various application fields. We present here the use of asymptotic expansions for linear elliptic problems to derive and justify so-called ap-proximate or effective boundary conditions. We first recall the known results of the literature, and then discuss the optimality of the error estimates in the smooth case. For non-smooth geometries, the results of [18, 57] are commented and adapted to a model problem, and two improvements of the approximate model are proposed to increase its numerical performance.
Résumé
Les problèmes faisant intervenir des matériaux avec couches minces sont fréquemment rencontrés dans divers domaines d’application. On présente ici la dérivation et la justification de conditions aux limites approchées, à l’aide de techniques de développements asymptotiques. Aprés avoir rappelé les résultats connus dans la littérature, on discute l’optimalité des estimations d’erreurs dans le cas d’une géométrie régulière. Dans le cas non régulier, les résultats obtenus dans [18, 57] sont commentés et adaptés au cas d’étude. Deux améliorations de la condition approchée sont proposées pour augmenter le taux de convergence.
© EDP Sciences, SMAI 2018
This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.