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• W2132400089 abstract "This note deals with localized approximations of homogenized coefficients of second order divergence form elliptic operators with random statistically homogeneous coefficients, by means of “periodization” and other “cut-off” procedures. For instance in the case of periodic approximation, we consider a cubic sample [0,ρ]d of the random medium, extend it periodically in Rd and use the effective coefficients of the obtained periodic operators as an approximation of the effective coefficients of the original random operator. It is shown that this approximation converges a.s., as ρ→∞, and gives back the effective coefficients of the original random operator. Moreover, under additional mixing conditions on the coefficients, the rate of convergence can be estimated by some negative power of ρ which only depends on the dimension, the ellipticity constant and the rate of decay of the mixing coefficients. Similar results are established for approximations in terms of appropriate Dirichlet and Neumann problems localized in a cubic sample [0,ρ]d. Nous étudions différentes procédures de périodisation ou troncature pour approcher les coefficients effectifs d'un opérateur elliptique du second ordre à coefficients aléatoires stationnaires. Considérons par exemple la restriction d'un environnement aléatoire à un cube [0,ρ]d et son prolongement périodique à Rd tout entier. Nous montrons qu'alors, pour presque toute réalisation de l'environnement aléatoire, les coefficients homogénéisés dans l'approximation périodique convergent quand ρ→∞ vers les coefficients effectifs de l'opérateur initial. Sous des hypothèses de mélange nous prouvons des bornes sur la vitesse de convergence de la forme ρ−α où α>0 ne dépend que de la dimension, la constante d'ellipticité et du taux de mélange. Nous obtenons aussi des résultats similaires pour des approximations basées sur des problèmes de Neumann ou de Dirichlet, localisées dans un cube [0,ρ]d." @default.
• W2132400089 created "2016-06-24" @default.
• W2132400089 creator A5049188158 @default.
• W2132400089 creator A5054322468 @default.
• W2132400089 date "2004-04-01" @default.
• W2132400089 modified "2023-10-15" @default.
• W2132400089 title "Approximations of effective coefficients in stochastic homogenization" @default.
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• W2132400089 doi "https://doi.org/10.1016/j.anihpb.2003.07.003" @default.
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