A posteriori error bounds for finite element approximations of time-dependent mean field games (opens in new tab)

We present a posteriori error bounds for a general class of stabilized finite element approximations of time-dependent mean field games. We first show the equivalence between the norm of the error and the dual norm of the residual in the coupled Hamilton-Jacobi-Bellman and Kolmogorov-Fokker-Planck equations. We then derive a reliable and efficient a posteriori error estimator that is based on residual estimators, along with the temporal jump est...