Convergence of approximation schemes for fully nonlinear second order equations

Article type: Research Article

Authors: Barles, G. | Souganidis, P.E.

Affiliations: CEREMADE, University of Paris-Dauphine, Place De Lattre de Tassigny, 75775 Paris Cedex 16, France | Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, RI 02912, USA

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.

DOI: 10.3233/ASY-1991-4305

Journal: Asymptotic Analysis, vol. 4, no. 3, pp. 271-283, 1991