Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★

Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★

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 the...

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Main Authors: Auvray Alexis, Vial Grégory
Format: Article
Language:English
Published: EDP Sciences 2018-01-01
Series:ESAIM: Proceedings and Surveys
Online Access:https://doi.org/10.1051/proc/201861038
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spelling doaj-be0464caac294090bea3593f3fb326272021-07-15T14:14:22ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592018-01-0161385410.1051/proc/201861038proc_esaim2018_038Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★Auvray AlexisVial GrégoryProblems 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.https://doi.org/10.1051/proc/201861038
collection DOAJ
language English
format Article
sources DOAJ
author Auvray Alexis
Vial Grégory
spellingShingle Auvray Alexis
Vial Grégory
Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★
ESAIM: Proceedings and Surveys
author_facet Auvray Alexis
Vial Grégory
author_sort Auvray Alexis
title Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★
title_short Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★
title_full Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★
title_fullStr Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★
title_full_unstemmed Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★
title_sort asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★
publisher EDP Sciences
series ESAIM: Proceedings and Surveys
issn 2267-3059
publishDate 2018-01-01
description 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.
url https://doi.org/10.1051/proc/201861038
work_keys_str_mv AT auvrayalexis asymptoticexpansionsandeffectiveboundaryconditionsashortreviewforsmoothandnonsmoothgeometrieswiththinlayers
AT vialgregory asymptoticexpansionsandeffectiveboundaryconditionsashortreviewforsmoothandnonsmoothgeometrieswiththinlayers
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