Report 2001-09

Sparse Two-Scale FEM for Homogenization Problems

A.-M. Matache

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

Paper: Available as PDF (281 KB) or as hardcopy to order reports@sam.math.ethz.ch.

Publishing information: J. Sci. Comput., 17, No. 1-4, 659-669 (2002)