MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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.

Feb 18, 2003
Feb 18, 2003
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