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Two-Scale FEM for Homogenization Problems

by A. M. Matache and Ch. Schwab

(Report number 2001-06)

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

Keywords:

@Techreport{MS01_283,
  author = {A. M. Matache and Ch. Schwab},
  title = {Two-Scale FEM for Homogenization Problems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2001-06},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2001/2001-06.pdf },
  year = {2001}
}

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