[Décroissance exponentielle de l'erreur de résonance en homogénéisation numerique via des problèmes de cellules paraboliques et elliptiques]
Cette note présente deux nouvelles approches pour trouver les coefficients homogénéisés des EDP elliptiques multi-échelles. Les approches standard pour calculer les coefficients homogénéisés souffrent de ce que l'on appelle l'erreur de résonance, qui découle d'une inadéquation entre les vraies conditions aux limites et celles computationelles. Nos nouvelles méthodes, basées sur des solutions aux problèmes de cellules paraboliques et elliptiques, entraînent une décroissance exponentielle de l'erreur de résonance.
This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the true and the computational boundary conditions. Our new methods, based on solutions of parabolic and elliptic cell problems, result in an exponential decay of the resonance error.
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@article{CRMATH_2019__357_6_545_0,
author = {Abdulle, Assyr and Arjmand, Doghonay and Paganoni, Edoardo},
title = {Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems},
journal = {Comptes Rendus. Math\'ematique},
pages = {545--551},
publisher = {Elsevier},
volume = {357},
number = {6},
year = {2019},
doi = {10.1016/j.crma.2019.05.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2019.05.011/}
}
TY - JOUR AU - Abdulle, Assyr AU - Arjmand, Doghonay AU - Paganoni, Edoardo TI - Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems JO - Comptes Rendus. Mathématique PY - 2019 SP - 545 EP - 551 VL - 357 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2019.05.011/ DO - 10.1016/j.crma.2019.05.011 LA - en ID - CRMATH_2019__357_6_545_0 ER -
%0 Journal Article %A Abdulle, Assyr %A Arjmand, Doghonay %A Paganoni, Edoardo %T Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems %J Comptes Rendus. Mathématique %D 2019 %P 545-551 %V 357 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2019.05.011/ %R 10.1016/j.crma.2019.05.011 %G en %F CRMATH_2019__357_6_545_0
Abdulle, Assyr; Arjmand, Doghonay; Paganoni, Edoardo. Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems. Comptes Rendus. Mathématique, Tome 357 (2019) no. 6, pp. 545-551. doi : 10.1016/j.crma.2019.05.011. http://www.numdam.org/articles/10.1016/j.crma.2019.05.011/
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☆ This work is partially supported by the Swiss National Science Foundation, grant No. 200020_172710. The authors thank Jean-Christophe Mourrat for useful discussions.
