Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians

Abstract

We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal Lipschitz domains with strongly monotone running costs. In particular, we obtain a rate of convergence in the $H^1$-norm for the value function approximations and in the $L^2$-norm for the approximations of the density. We also establish a rate of convergence for the error between the exact solution of the MFG system with a nondifferentiable Hamiltonian and the finite element discretizations of the corresponding MFG system with a regularized Hamiltonian.

31 pages

References in corpus (6)

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• Second order local minimal-time Mean Field Games
• Finite element approximation of time-dependent mean field games with nondifferentiable Hamiltonians
• Near and full quasi-optimality of finite element approximations of stationary second-order mean field games
• Regularization of Stationary Second-order Mean Field Game Partial Differential Inclusions
• A posteriori error bounds for finite element approximations of steady-state mean field games