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

- Songting Luo, Yifeng Yu, Hongkai Zhao
- Multiscale Modeling & Simulation
- 2011

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@article{Gomes2004ComputingTE, title={Computing the Effective Hamiltonian using a Variational Approach}, author={Diogo A. Gomes and Adam M. Oberman}, journal={Proceedings of the 44th IEEE Conference on Decision and Control}, year={2004}, pages={729-733} }

- Published 2004 in Proceedings of the 44th IEEE Conference on…
DOI:10.1137/S0363012902417620

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.

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