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A Lagrange-Galerkin scheme for first order mean field games systems (2303.14941v1)
Published 27 Mar 2023 in math.AP, cs.NA, math.NA, and math.OC
Abstract: In this work, we consider a first order mean field games system with non-local 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 dimension one and two.