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Journal of Nonlinear Science

, Volume 14, Issue 3, pp 279–296 | Cite as

On the Γ-convergence of discrete dynamics and variational integrators

  • S. Müller
  • M. Ortiz
Article

Summary

For a simple class of Lagrangians and variational integrators, derived by time discretization of the action functional, we establish (i) the Γ-convergence of the discrete action sum to the action functional; (ii) the relation between Γ-convergence and weak* convergence of the discrete trajectories in {itW{su1,℞}}({ofR};{ofr{sun}; and (iii) the relation between Γ-convergence and the convergence of the Fourier transform of the discrete trajectories as measured in the flat norm.

Key words

discrete dynamics variational integrators Γ-convergence spectral convergence flat norm 

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Copyright information

© Springer-Verlag New York, LLC 2004

Authors and Affiliations

  • S. Müller
    • 1
  • M. Ortiz
    • 2
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaUSA

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