Two-scale FEM for homogenization problems
ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 4, pp. 537-572.

The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale ε1 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.

DOI : 10.1051/m2an:2002025
Classification : 65N30
Mots clés : homogenization, two-scale regularity, finite element method (FEM), two-scale FEM
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     title = {Two-scale {FEM} for homogenization problems},
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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://archive.numdam.org/articles/10.1051/m2an:2002025/

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