Improving on computation of homogenized coefficients in the  periodic and quasi-periodic settings

Xavier Blanc; Claude Le Bris

doi:10.3934/nhm.2010.5.1

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2010, Volume 5, Issue 1: 1-29. Doi: 10.3934/nhm.2010.5.1

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Improving on computation of homogenized coefficients in the periodic and quasi-periodic settings

Xavier Blanc^1, and
Claude Le Bris^2,

1.
Laboratoire J. L. Lions, Université Pierre et Marie Curie, Boî te courrier 187, F-75252 Paris
2.
Université Paris-Est, CERMICS, Ecole Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne-la-Valléauthore Cedex 2

Received: April 30, 2009

Revised: September 30, 2009

Published: February 2010

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Abstract

In quasi-periodic homogenization of elliptic equations or nonlinear periodic homogenization of systems, the cell problem must be in general set on the whole space. Numerically computing the homogenization coefficient therefore implies a truncation error, due to the fact that the problem is approximated on a bounded, large domain. We present here an approach that improves the rate of convergence of this approximation.

Keywords:

homogenization; cell problem; quasi-convex; quasi-periodic; elliptic equation; nonlinear; hyperelasticity.

Mathematics Subject Classification: 35B27, 35Q74, 34B15, 74Q05.

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