Titre :

Random walk in random environment, corrector equation and homogenized coefficients: from theory to numerics, back and forth

Auteur(s) :

Egloffe, Anne-Claire [Auteur]
Numerical simulation of biological flows [REO]
Gloria, Antoine [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de Mathématique [Bruxelles] [ULB]
Mourrat, Jean-Christophe [Auteur]
Département de Mathématiques - EPFL
Nguyen, Thahn Nhan [Auteur]
Ton Duc Thang University [Hô-Chi-Minh-City]

Titre de la revue :

IMA Journal of Numerical Analysis

Pagination :

44

Éditeur :

Oxford University Press (OUP)

Date de publication :

2014

ISSN :

0272-4979

Discipline(s) HAL :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

Résumé en anglais : [en]

This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by ...
Lire la suite >This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions on quantitative stochastic homogenization theory by two of us and by Otto. This article makes the connection between our theoretical results and computations. We give a complete picture of the numerical methods found in the literature, compare them in terms of known (or expected) convergence rates, and study them numerically. Two types of methods are presented: methods based on the corrector equation, and methods based on random walks in random environments. The numerical study confirms the sharpness of the analysis (which it completes by making precise the prefactors, next to the convergence rates), supports some of our conjectures, and calls for new theoretical developments.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Méthodes asymptotiques appliquées à la science des matériaux

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL