Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite element method in the spirit of the localized orthogonal decomposition, that is especially efficient when the negative and positive materials exhibit multiscale features. We derive optimal linear convergence in the energy norm independently of the potentially low regularity of the exact solution. Numerical experiments illustrate the theoretical convergence rates and show the applicability of the method for a large class of sign-changing diffusion problems.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2021007
Keywords: Generalized finite element method, multiscale method, sign-changing coefficients, T-coercivity
@article{M2AN_2021__55_3_939_0,
author = {Chaumont-Frelet, Th\'eophile and Verf\"urth, Barbara},
title = {A generalized finite element method for problems with sign-changing coefficients},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {939--967},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {3},
doi = {10.1051/m2an/2021007},
mrnumber = {4253164},
zbl = {1477.65201},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021007/}
}
TY - JOUR AU - Chaumont-Frelet, Théophile AU - Verfürth, Barbara TI - A generalized finite element method for problems with sign-changing coefficients JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 939 EP - 967 VL - 55 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021007/ DO - 10.1051/m2an/2021007 LA - en ID - M2AN_2021__55_3_939_0 ER -
%0 Journal Article %A Chaumont-Frelet, Théophile %A Verfürth, Barbara %T A generalized finite element method for problems with sign-changing coefficients %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 939-967 %V 55 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021007/ %R 10.1051/m2an/2021007 %G en %F M2AN_2021__55_3_939_0
Chaumont-Frelet, Théophile; Verfürth, Barbara. A generalized finite element method for problems with sign-changing coefficients. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 3, pp. 939-967. doi: 10.1051/m2an/2021007
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