Convergence of approximation schemes for fully nonlinear second order equations

Abstract

We present a simple, purely analytic method for proving the convergence of a wide class of approximation schemes to the solution of fully non linear second-order elliptic or parabolic PDE. Roughly speaking, we prove that any monotone, stable and consistent scheme converges to the correct solution provided that there exists a comparison principle for the limiting equation. This method is based on the notion of viscosity solution of Crandall and Lions and it gives completely new results concerning the convergence of numerical schemes for stochastic differential games.