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arXiv · 2506.03039

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

Yohance A. P. Osborne·Iain Smears
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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.

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Yohance A. P. Osborne, Iain Smears. 2025-06-03. Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians. https://doi.org/10.1090/mcom%2F4189

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