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On the Γ-Convergence of Discrete Dynamics and Variational Integrators

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Abstract

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 W1,\inftyR; Rn); 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, Pasadena, CA 90025, USA

    M. Ortiz

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  1. S. Müller
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  2. M. Ortiz
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Correspondence to M. Ortiz.

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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/s00332-004-0585-1

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  • DOI: https://doi.org/10.1007/s00332-004-0585-1

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