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Sparse Two-Scale FEM for Homogenization Problems

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Abstract

We analyze two-scale Finite Element Methods for the numerical solution of elliptic homogenization problems with coefficients oscillating at a small length scale ε≪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 ε) 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.

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  1. Seminar for Applied Mathematics, ETH-Zentrum, CH-8092, Zürich, Switzerland

    A.-M. Matache

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  1. A.-M. Matache
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Matache, AM. Sparse Two-Scale FEM for Homogenization Problems. Journal of Scientific Computing 17, 659–669 (2002). https://doi.org/10.1023/A:1015187000835

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