Title :

An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations

Author(s) :

Gloria, Antoine [Auteur]
Département de Mathématique [Bruxelles] [ULB]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Neukamm, Stefan [Auteur]
Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] [WIAS]
Otto, Felix [Auteur]
Max Planck Institute for Mathematics in the Sciences [MPI-MiS]

Journal title :

ESAIM: Mathematical Modelling and Numerical Analysis

Pages :

325-346

Publisher :

EDP Sciences

Publication date :

2014-01-21

ISSN :

0764-583X

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

We establish an optimal, linear rate of convergence for the stochastic homogenization of discrete linear elliptic equations. We consider the model problem of independent and identically distributed coefficients on a ...
Show more >We establish an optimal, linear rate of convergence for the stochastic homogenization of discrete linear elliptic equations. We consider the model problem of independent and identically distributed coefficients on a discretized unit torus. We show that the difference between the solution to the random problem on the discretized torus and the first two terms of the two-scale asymptotic expansion has the same scaling as in the periodic case. In particular the $L^2$-norm in probability of the \mbox{$H^1$-norm} in space of this error scales like $\epsilon$, where $\epsilon$ is the discretization parameter of the unit torus. The proof makes extensive use of previous results by the authors, and of recent annealed estimates on the Green's function by Marahrens and the third author.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL