On a Variational Approximation of the Effective Hamiltonian

The approximation of the effective Hamiltonian is a challenging problem with a strong impact on many applications e.g. to the study of dynamical systems, weak KAM theory, homogenization, mass transfer problems. In this paper we present a numerical approximation of the variational approach proposed by C. Evans in [4], discuss its consistency and give some hints regarding its implementation. Finally, we compare this approach to the numerical implementation of the min-max formula proposed by Gomes and Oberman [6].