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Two-scale FEM for homogenization problems

Published online by Cambridge University Press:  15 September 2002

Ana-Maria Matache
Seminar for Applied Mathematics, ETH-Zentrum, CH-8092 Zürich, Switzerland.
Christoph Schwab
Seminar for Applied Mathematics, ETH-Zentrum, CH-8092 Zürich, Switzerland.
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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.

Research Article
© EDP Sciences, SMAI, 2002

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