An Approximation Scheme for Evolutive Hamilton-Jacobi Equations

An approximation scheme for the evolutive Hamilton-Jacobi equation associated with the nite horizon deterministic problem is presented. The scheme allows a variable time step and can be applied to structured and unstructured grids. Depending on the regularity of the value function di erent orders of convergence are proved. In particular, under Lipschitz assumptions the convergence behavior of conservative monotone hyperbolic schemes is retrieved. Namely, if k h constant then we have convergence of order 12 , where k and h are the space and the time step, respectively.