In this work, we consider a first order mean field game system with nonlocal couplings. A Lagrange–Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton–Jacobi–Bellman equation, is proposed to discretize the mean field games system. The convergence of solutions to the scheme towards a solution to the mean field game system is established in arbitrary space dimensions. The scheme is implemented to approximate two mean field games systems in dimensions one and two.
A Lagrange–Galerkin Scheme for First Order Mean Field Game Systems / Carlini, Elisabetta; Silva, Francisco J.; Zorkot, Ahmad. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 62:1(2024), pp. -198. [10.1137/23M1561762]
A Lagrange–Galerkin Scheme for First Order Mean Field Game Systems
Carlini, Elisabetta;
2024
Abstract
In this work, we consider a first order mean field game system with nonlocal couplings. A Lagrange–Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton–Jacobi–Bellman equation, is proposed to discretize the mean field games system. The convergence of solutions to the scheme towards a solution to the mean field game system is established in arbitrary space dimensions. The scheme is implemented to approximate two mean field games systems in dimensions one and two.| File | Dimensione | Formato | |
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