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.
Classification : 65N30
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: Mathematical Modelling and Numerical Analysis - 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},
zbl = {1070.65572},
mrnumber = {1932304},
language = {en},
url = {archive.numdam.org/item/M2AN_2002__36_4_537_0/}
}
Matache, Ana-Maria; Schwab, Christoph. Two-scale FEM for homogenization problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002) no. 4, pp. 537-572. doi : 10.1051/m2an:2002025. http://archive.numdam.org/item/M2AN_2002__36_4_537_0/
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