Two-scale FEM for homogenization problems

Matache, Ana-Maria; Schwab, Christoph

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 4, p. 537-572

Abstract

The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale $ε ≪ 1$ is analyzed. Full elliptic regularity independent of $ε$ 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 $ε$ scale of the solution with work independent of $ε$ and without analytical homogenization are introduced. Robust in $ε$ error estimates for the two-scale FE spaces are proved. Numerical experiments confirm the theoretical analysis.

MR 1932304 | Zbl 1070.65572

DOI : https://doi.org/10.1051/m2an:2002025
Classification: 65N30
Keywords: 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},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     year = {2002},
     pages = {537-572},
     doi = {10.1051/m2an:2002025},
     zbl = {1070.65572},
     mrnumber = {1932304},
     language = {en},
     url = {http://www.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, Volume 36 (2002) no. 4, pp. 537-572. doi : 10.1051/m2an:2002025. http://www.numdam.org/item/M2AN_2002__36_4_537_0/

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