The purpose of this work is to investigate the behavior of Multiscale Finite Element type methods for advection-diffusion problems in the advection-dominated regime. We present, study and compare various options to address the issue of the simultaneous presence of both heterogeneity of scales and strong advection. Classical MsFEM methods are compared with adjusted MsFEM methods, stabilized versions of the methods, and a splitting method that treats the multiscale diffusion and the strong advection separately.
Accepté le :
DOI : 10.1051/m2an/2016057
Mots clés : Homogenization, finite elements, highly oscillatory PDEs, advection-dominated problems
@article{M2AN_2017__51_3_851_0,
author = {Le Bris, Claude and Legoll, Fr\'ed\'eric and Madiot, Fran\c{c}ois},
title = {A numerical comparison of some {Multiscale} {Finite} {Element} approaches for advection-dominated problems in heterogeneous media},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {851--888},
publisher = {EDP-Sciences},
volume = {51},
number = {3},
year = {2017},
doi = {10.1051/m2an/2016057},
mrnumber = {3666649},
zbl = {1373.65083},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2016057/}
}
TY - JOUR AU - Le Bris, Claude AU - Legoll, Frédéric AU - Madiot, François TI - A numerical comparison of some Multiscale Finite Element approaches for advection-dominated problems in heterogeneous media JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 851 EP - 888 VL - 51 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016057/ DO - 10.1051/m2an/2016057 LA - en ID - M2AN_2017__51_3_851_0 ER -
%0 Journal Article %A Le Bris, Claude %A Legoll, Frédéric %A Madiot, François %T A numerical comparison of some Multiscale Finite Element approaches for advection-dominated problems in heterogeneous media %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 851-888 %V 51 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016057/ %R 10.1051/m2an/2016057 %G en %F M2AN_2017__51_3_851_0
Le Bris, Claude; Legoll, Frédéric; Madiot, François. A numerical comparison of some Multiscale Finite Element approaches for advection-dominated problems in heterogeneous media. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 851-888. doi : 10.1051/m2an/2016057. http://www.numdam.org/articles/10.1051/m2an/2016057/
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