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MiS Preprint
15/2003
On the $\Gamma$-Convergence of Discrete Dynamics and Variational Integrators
Stefan Müller and Michael Ortiz
Abstract
For a simple class of Lagrangians and variational integrators, derived by time discretization of the action functional, we supply conditions ensuring: i) The $\Gamma$-convergence of the discrete action sum to the action functional; ii) The weak$^*$ convergence of the discrete trajectories in $W^{1,\infty}({\mathbb{R}})$ and uniform convergence on compact subsets; and iii) The convergence of the Fourier transform of the discrete trajectories as measures in the flat norm.
