  We study the iterative algorithm proposed by S. Armstrong, A. Hannukainen, T.
Kuusi, J.-C. Mourrat to solve elliptic equations in divergence form with
stochastic stationary coefficients. Such equations display rapidly oscillating
coefficients and thus usually require very expensive numerical calculations,
while this iterative method is comparatively easy to compute. In this article,
we strengthen the estimate for the contraction factor achieved by one iteration
of the algorithm. We obtain an estimate that holds uniformly over the initial
function in the iteration, and which grows only logarithmically with the size
of the domain.
