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

Elisabetta Carlini (1) , Francisco J. Silva (2)

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
2 Dipartimento di Matematica "Guido Castelnuovo", Università Roma La Sapienza

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.

Domaines: Analyse numérique [math.NA]

Elisabetta Carlini, Francisco J. Silva. A fully-discrete Semi-Lagrangian scheme for a first order mean field game problem. 2012. ⟨hal-00800507⟩