On the G-Convergence of Discrete Dynamics and Variational Integrators

For a simple class of Lagrangians and variational integrators, derived by time discretization of the action functional, we establish (i) the -convergence of the discrete action sum to the action functional; (ii) the relation between -convergence and weak∗ convergence of the discrete trajectories in W 1,∞(R;Rn); and (iii) the relation between -convergence and the convergence of the Fourier transform of the discrete trajectories as measured in the flat norm.