Geodesic
Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers
Alexis Auvray1 ; Grégory Vial1
1 Univ 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.

Voir la notice de l'article provenant de 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.
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 
@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},
     publisher = {mathdoc},
     volume = {61},
     year = {2018},
     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
PB  - mathdoc
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
%I mathdoc
%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. http://geodesic.mathdoc.fr/articles/10.1051/proc/201861038/

Cité par Sources :