A New Approximation for Effective Hamiltonians for Homogenization of a class of Hamilton–Jacobi Equations
Songting Luo, Yifeng Yu, Hongkai Zhao · Multiscale Modeling and Simulation · 2011
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 [Formula: see text] for all [Formula: see text]. Error estimates and stability are proved and numerical examples are presented to demonstrate the performance.