Special Session 27: Mathematical problems in economics, materials and life science: Analysis and simulation of nonlinear multiscale dynamics
Contents
Consider a discrete elliptic equation on the discrete torus of size $L$, with iid conductivities. We show that the $L^2$-norm in probability of the discrete $H^1$-norm in space of the first two terms of the two-scale expansion decays with the same rate as in the case of deterministic, periodic coefficients (up to a logarithm in dimension 2). The proof relies on moment bounds on the corrector and its gradient and an optimal estimate of the error on the approximation of the homogenized coefficients by periodization.