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 formula11-convergence of the discrete action sum to the action functional; ii) The weakformula13 convergence of the discrete trajectories in formula15 and uniform convergence on compact subsets; and iii) The convergence of the Fourier transform of the discrete trajectories as measures in the flat norm.

18.10.2019, 02:12