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Two-scale FEM for homogenization problems

Published online by Cambridge University Press:  15 September 2002

Ana-Maria Matache  and
Christoph Schwab
Ana-Maria Matache
Affiliation:
Seminar for Applied Mathematics, ETH-Zentrum, CH-8092 Zürich, Switzerland. schwab@sam.math.ethz.ch.
Christoph Schwab
Affiliation:
Seminar for Applied Mathematics, ETH-Zentrum, CH-8092 Zürich, Switzerland. schwab@sam.math.ethz.ch.
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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 shownwhen 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 thesolution with work independent of ε and withoutanalytical homogenization are introduced. Robustin ε error estimates for the two-scale FE spaces are proved. Numerical experiments confirm thetheoretical analysis.

Keywords

Homogenizationtwo-scale regularityFinite Element Method (FEM)two-scale FEM.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 4 , July 2002 , pp. 537 - 572
Copyright
© EDP Sciences, SMAI, 2002

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