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 Barron and Jensen [Comm. Partial Differential Equations, 15 (1990), pp. 1713-1742] 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 <(H(SIC))over bar>(p) for all p. Error estimates and stability are proved and numerical examples are presented to demonstrate the performance.