Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs

We consider periodic homogenization of the fully nonlinear uniformly elliptic equation u(epsilon) + H(x, x/epsilon, Du(epsilon), D(2)u(epsilon)) = 0. We give an estimate of the rate of convergence of ue to the solution u of the homogenized problem u + (H) over bar (x, Du, D(2)u) = 0. Moreover we describe a numerical scheme for the approximation of the effective nonlinearity (H) over bar and we estimate the corresponding rate of convergence