

Preprint 15/2003
On the Γ-Convergence of Discrete Dynamics and Variational Integrators
Stefan Müller and Michael Ortiz
Contact the author: Please use for correspondence this email.
Submission date: 18. Feb. 2003
Pages: 14
published in: Journal of nonlinear science, 14 (2004) 3, p. 279-296
DOI number (of the published article): 10.1007/BF02666023
Bibtex
Keywords and phrases: discrete dynamics, variational integrators, gamma-convergence, spectral convergence, flat norm
Download full preprint: PDF (216 kB), PS ziped (212 kB)
Abstract:
For a simple class of Lagrangians and variational integrators,
derived by time discretization of the action functional, we supply
conditions ensuring: i) The -convergence of the discrete
action sum to the action functional; ii) The weak
convergence of the discrete trajectories in
and uniform convergence on compact
subsets; and iii) The convergence of the Fourier transform of the
discrete trajectories as measures in the flat norm.