A New Approximation for Effective Hamiltonians for Homogenization of a class of Hamilton-Jacobi Equations

We propose a new formulation to compute effective Hamiltonians for homogenization of a class of Hamilton-Jacobi equations. Our formulation utilizes an observation made by BarronJensen [3] about viscosity supersolutions of Hamilton-Jacobi equations. The key idea is to link the effective Hamiltonian to a suitable effective equation. The main advantage of our formulation is that only one auxiliary equation needs to be solved in order to compute the effective Hamiltonian H̄(p) for all p. Error estimates and stability are proved and numerical examples are presented to demonstrate the performance.