# Spectral measure and approximation of homogenized coefficients

1 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation formula to design and analyze effective and computable approximations of the homogenized coefficients. In particular, we show that information on the edge of the spectrum of the generator of the environment viewed by the particle projected on the local drift yields bounds on the approximation error, and conversely. Combined with results by Otto and the first author in low dimension, and results by the second author in high dimension, this allows us to prove that for any dimension $d\geq 2$, there exists an explicit numerical strategy to approximate homogenized coefficients which converges at the rate of the central limit theorem.
Document type :
Journal articles

Cited literature [19 references]

https://hal.inria.fr/inria-00510513
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Submitted on : Sunday, May 22, 2011 - 10:51:55 AM
Last modification on : Wednesday, March 23, 2022 - 3:50:58 PM
Long-term archiving on: : Tuesday, August 23, 2011 - 2:20:45 AM

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### Citation

Antoine Gloria, Jean-Christophe Mourrat. Spectral measure and approximation of homogenized coefficients. Probability Theory and Related Fields, Springer Verlag, 2012, 154, pp.287-326. ⟨10.1007/s00440-011-0370-7⟩. ⟨inria-00510513v2⟩

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