On the Γ-convergence of discrete dynamics and variational integrators

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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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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Key words

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