Geodesic
Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers
Alexis Auvray1 ; Grégory Vial1
1Univ Lyon, École centrale de Lyon, CNRS UMR 5208, Institut Camille Jordan, 36 avenue Guy de Collongue, Écully Cedex, F-69134, France
ESAIM. Proceedings, Tome 61 (2018), pp. 38-54
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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.
DOI : 10.1051/proc/201861038

Alexis Auvray  1   ; Grégory Vial  1

1 Univ Lyon, École centrale de Lyon, CNRS UMR 5208, Institut Camille Jordan, 36 avenue Guy de Collongue, Écully Cedex, F-69134, France 
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     title = {Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers},
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Alexis Auvray; Grégory Vial. Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers. ESAIM. Proceedings, Tome 61 (2018), pp. 38-54. doi: 10.1051/proc/201861038

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