Abstract
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.
Research supported by the Swiss National Foundation under Project Number BBW 21-58754.99
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Schwab, C. (2002). Two Scale FEM for Homogenization Problems. In: Babuška, I., Ciarlet, P.G., Miyoshi, T. (eds) Mathematical Modeling and Numerical Simulation in Continuum Mechanics. Lecture Notes in Computational Science and Engineering, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56288-4_7
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DOI: https://doi.org/10.1007/978-3-642-56288-4_7
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