The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale is analyzed. Full elliptic regularity independent of is shown when the solution is viewed as mapping from the slow into the fast scale. Two-scale FE spaces which are able to resolve the scale of the solution with work independent of and without analytical homogenization are introduced. Robust in error estimates for the two-scale FE spaces are proved. Numerical experiments confirm the theoretical analysis.
Mots-clés : homogenization, two-scale regularity, finite element method (FEM), two-scale FEM
@article{M2AN_2002__36_4_537_0,
author = {Matache, Ana-Maria and Schwab, Christoph},
title = {Two-scale {FEM} for homogenization problems},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {537--572},
publisher = {EDP-Sciences},
volume = {36},
number = {4},
year = {2002},
doi = {10.1051/m2an:2002025},
mrnumber = {1932304},
zbl = {1070.65572},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2002025/}
}
TY - JOUR AU - Matache, Ana-Maria AU - Schwab, Christoph TI - Two-scale FEM for homogenization problems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2002 SP - 537 EP - 572 VL - 36 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2002025/ DO - 10.1051/m2an:2002025 LA - en ID - M2AN_2002__36_4_537_0 ER -
%0 Journal Article %A Matache, Ana-Maria %A Schwab, Christoph %T Two-scale FEM for homogenization problems %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 537-572 %V 36 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2002025/ %R 10.1051/m2an:2002025 %G en %F M2AN_2002__36_4_537_0
Matache, Ana-Maria; Schwab, Christoph. Two-scale FEM for homogenization problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 4, pp. 537-572. doi : 10.1051/m2an:2002025. http://www.numdam.org/articles/10.1051/m2an:2002025/
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