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Mean-field games (MFGs) have shown strong modeling capabilities for largesystems in various fields, driving growth in computational methods formean-field game problems. However, high order methods have not been thoroughlyinvestigated. In this work, we explore applying general high-order numericalschemes with finite element methods in the space-time domain for computing theoptimal transport (OT), mean-field planning (MFP), and MFG problems. We conductseveral experiments to validate the convergence rate of the high order methodnumerically. Those numerical experiments also demonstrate the efficiency andeffectiveness of our approach.

High order computation of optimal transport, mean field planning, and mean field games