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Published in:
2002 | OriginalPaper | Chapter
Two Scale FEM for Homogenization Problems
Author : Christoph Schwab
Published in: Mathematical Modeling and Numerical Simulation in Continuum Mechanics
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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We analyze generalized Finite Element Methods for the numerical solution of elliptic problems with coefficients or geometries which are oscillating at a small length scale ɛ. Two-scale elliptic regularity results which are uniform in ɛ are presented. Two-scale FE spaces are introduced with error estimates that are uniform in ɛ. They resolve the ɛ scale of the solution with work independent of ɛ and without analytical homogenizations. Numerical experiments confirming the theory are presented.