On the -Convergence of Discrete Dynamics and Variational Integrators

Stefan Müller, and Michael Ortiz
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Submission date: 18. Feb. 2003
Pages: 14
published in: Journal of nonlinear science, 14 (2004) 3, p. 279-296 
Keywords and phrases: discrete dynamics, variational integrators, gamma-convergence, spectral convergence, flat norm
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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.