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On the Γ-convergence of discrete dynamics and variational integrators

Journal of Nonlinear Science volume 14, pages 279–296 (2004)Cite this 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.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany

    S. Müller

  2. Division of Engineering and Applied Science, California Institute of Technology, 90025, Pasadena, CA, USA

    M. Ortiz

Authors
  1. S. Müller
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  2. M. Ortiz
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Communicated by J. E. Marsden and R. Kohn

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Müller, S., Ortiz, M. On the Γ-convergence of discrete dynamics and variational integrators. J Nonlinear Sci 14, 279–296 (2004). https://doi.org/10.1007/BF02666023

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  • DOI: https://doi.org/10.1007/BF02666023

Key words

  • discrete dynamics
  • variational integrators
  • Γ-convergence
  • spectral convergence
  • flat norm