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

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March 2010, 5(1): 1-29. doi: 10.3934/nhm.2010.5.1

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

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

Received May 2009 Revised October 2009 Published February 2010

Abstract
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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, 74Q0.

Citation: Xavier Blanc, Claude Le Bris. Improving on computation of homogenized coefficients in the periodic and quasi-periodic settings. Networks & Heterogeneous Media, 2010, 5 (1) : 1-29. doi: 10.3934/nhm.2010.5.1

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