An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation

In this paper an adaptive finite difference scheme for the solution of the discrete first order Hamilton-Jacobi-Bellman equation is presented, Local a posteriori error estimates are established and certain properties of these estimates are proved. Based on these estimates an adapting iteration for the discretization of the state space is developed. An implementation of the scheme for two-dimensional grids is given and numerical examples are discussed.