A fully-discrete Semi-Lagrangian scheme for a first order mean field game problem

Elisabetta Carlini (1) , Francisco José Silva (2)

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
2 XLIM-DMI - DMI

In this work we propose a fully-discrete Semi-Lagrangian scheme for a first order mean field game system. We prove that the resulting discretization admits at least one solution and, in the scalar case, we prove a convergence result for the scheme. Numerical simulations and examples are also discussed.

Mots clés: Mean field games; First order system; Semi-Lagrangian schemes; Numerical methods

Domaines: Optimisation et contrôle [math.OC]

Elisabetta Carlini, Francisco José Silva. A fully-discrete Semi-Lagrangian scheme for a first order mean field game problem. 2013. ⟨hal-00913721⟩