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MiS Preprint

On the $\Gamma$-Convergence of Discrete Dynamics and Variational Integrators

Stefan Müller and Michael Ortiz


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.

discrete dynamics, variational integrators, gamma-convergence, spectral convergence, flat norm

Related publications

2004 Repository Open Access
Stefan Müller and Michael Ortiz

On the \(\Gamma\)-convergence of discrete dynamics and variational integrators

In: Journal of nonlinear science, 14 (2004) 3, pp. 279-296