Value iteration convergence of ε-monotone schemes for stationary Hamilton-Jacobi equations

We present an abstract convergence result for the fixed point approximation of stationary Hamilton Jacobi equations. The basic assumptions on the discrete operator are invariance with respect to the addition of constants, epsilon-monotonicity and consistency. The result can be applied to various high-order approximation schemes which are illustrated in the paper. Several applications to Hamilton Jacobi equations and numerical tests are presented.