- Seminari
- Lagrange Galerkin schemes for Mean Field Games
Lagrange Galerkin schemes for Mean Field Games
Relatore
Elisabetta Carlini - Università La Sapienza, Roma
Data
27-apr-2023 - Ora:
15:30
Sala Verde (solo in presenza)
Abstract: We propose a numerical approximation of a mean-field game system with nonlocal couplings.
The system is characterized by a backward Hamilton-Jacobi-Bellman equation coupled with a forward Fokker-Planck equation.
The approximation is constructed by combining Lagrange-Galerkin techniques, for the FP equation, with semi-Lagrangian techniques, for the HJB equation.
The resulting discrete system is solved using fixed-point iterations.
The approximation is constructed by combining Lagrange-Galerkin techniques, for the FP equation, with semi-Lagrangian techniques, for the HJB equation.
The resulting discrete system is solved using fixed-point iterations.
We show that the scheme is conservative, consistent and stable for large time steps with respect to spatial steps. In the case of first-order MFG, we prove a convergence theorem for the exactly integrated Lagrange-Galerkin scheme in arbitrary spatial dimensions. In the case of second-order MFG, we construct an accurate high-order scheme. We propose an implementable version with inexact integration and finally show some numerical simulations.
- Data pubblicazione
- 19-apr-2023
- Referente
- Giacomo Albi
- Dipartimento
- Informatica
