Two-scale FEM for homogenization problems

Matache, Ana-Maria ; Schwab, Christoph

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 4, pp. 537-572.

Résumé

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

Détail

DOI : 10.1051/m2an:2002025

Classification : 65N30
Keywords: homogenization, two-scale regularity, finite element method (FEM), two-scale FEM

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