Gomes, Diogo A.; Oberman, Adam M. Computing the effective Hamiltonian using a variational approach. (English) Zbl 1081.49024 SIAM J. Control Optim. 43, No. 3, 792-812 (2004). Summary: A numerical method for homogenization of Hamilton–Jacobi equations is presented and implemented as an \(L^\infty\) 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. One and two dimensional examples are worked in detail, comparing known results with the numerical ones and computing new examples. The cases of nonstrictly convex Hamiltonians and Hamiltonians for which the cell problem has no solution are treated. Cited in 1 ReviewCited in 21 Documents MSC: 49M30 Other numerical methods in calculus of variations (MSC2010) 49L20 Dynamic programming in optimal control and differential games 37J50 Action-minimizing orbits and measures (MSC2010) 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 35F20 Nonlinear first-order PDEs Keywords:Hamilton-Jacobi equation; homogenization; numerics PDFBibTeX XMLCite \textit{D. A. Gomes} and \textit{A. M. Oberman}, SIAM J. Control Optim. 43, No. 3, 792--812 (2004; Zbl 1081.49024) Full Text: DOI