  We study the convergence of the Method of Reflections for the Dirichlet
problem of the Poisson and the Stokes equations in perforated domains which
consist in the exterior of balls. We prove that the method converges if the
balls are contained in a bounded region and the density of the electrostatic
capacity of the balls is sufficiently small. If the capacity density is too
large or the balls extend to the whole space, the method diverges, but we
provide a suitable modification of the method that converges to the solution of
the Dirichlet problem also in this case. We give new proofs of classical
homogenization results for the Dirichlet problem of the Poisson and the Stokes
equations in perforated domains using the (modified) Method of Reflections.
