| Abstract: |
| We consider the analysis of numerical methods for second-order mean field games. In the setting of nondifferentiable Hamiltonians, the system comprises the HJB equation for the value function and the KFP partial differential inclusion for the density of the players.
In the nondifferentiable setting, it is known from examples that one cannot expect any quantitative control on the error made in approximating the unknown drift term that appears in the differential inclusion.
Despite this difficulty, we prove a rate of convergence for finite element approximations for such MFG systems, on 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. |
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