Computing the Effective Hamiltonian using a Variational Approach

A numerical method for homogenization of Hamilton-Jacobi equations is presented and implemented as an L^∞calculus of variations problem. Solutions are found by solving a nonlinear convex optimization problem. The numerical method is shown to be convergent and error estimates are provided. Several examples are worked in detail, including the cases of non-strictly convex Hamiltonians and Hamiltonians for which the cell problem has no solution.