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
Cet article a éte moissonné depuis la source EDP Sciences
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.
@article{EP_2018_61_a2,
author = {Alexis Auvray and Gr\'egory Vial},
title = {Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers},
journal = {ESAIM. Proceedings},
pages = {38--54},
year = {2018},
volume = {61},
doi = {10.1051/proc/201861038},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201861038/}
}
TY - JOUR AU - Alexis Auvray AU - Grégory Vial TI - Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers JO - ESAIM. Proceedings PY - 2018 SP - 38 EP - 54 VL - 61 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201861038/ DO - 10.1051/proc/201861038 LA - en ID - EP_2018_61_a2 ER -
%0 Journal Article %A Alexis Auvray %A Grégory Vial %T Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers %J ESAIM. Proceedings %D 2018 %P 38-54 %V 61 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/201861038/ %R 10.1051/proc/201861038 %G en %F EP_2018_61_a2
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
Cité par Sources :