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Sparse Two-Scale FEM for Homogenization Problems

by A. M. Matache

(Report number 2001-09)

Abstract
We analyze two-scale Finite Element Methods for the numerical solution of elliptic homogenization problems with coefficients oscillating at a small length scale \varepsilon << 1. Based on a refined two-scale regularity on the solutions, two-scale tensor product FE spaces are introduced and error estimates which are robust (i.e. independent of \varepsilon) are given. We show that under additional two-scale regularity assumptions on the solution, resolution of the fine scale is possible with substantially fewer degrees of freedom and the two-scale full tensor product spaces can be "thinned out"" by means of sparse interpolation preserving at the same time the error estimates.

Keywords: Homogenization; two-scale FEM; sparse two-scale FEM

@Techreport{M01_286,
  author = {A. M. Matache},
  title = {Sparse Two-Scale FEM for Homogenization Problems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2001-09},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2001/2001-09.pdf },
  year = {2001}
}

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