Rate of convergence of a two-scale expansion for some "weakly" stochastic homogenization problems

TL;DR

This paper establishes a convergence rate for the two-scale expansion method applied to elliptic PDEs with random coefficients that are slight perturbations of periodic coefficients, advancing stochastic homogenization theory.

Contribution

It provides a quantitative rate of convergence for the two-scale expansion in stochastic homogenization with weakly random coefficients.

Findings

Derived explicit convergence rates for the two-scale expansion.

Applicable to elliptic PDEs with weakly random coefficients.

Enhances understanding of stochastic homogenization accuracy.

Abstract

We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of periodic coefficients.