Published May 2004
| public
Journal Article
On the Γ-convergence of discrete dynamics and variational integrators
- Creators
- Müller, S.
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Ortiz, M.
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 {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.
Additional Information
© Springer-Verlag New York, LLC 2004. Received May 22, 2003; accepted January 19, 2004. Online publication May 21, 2004. Communicated by J. E. Marsden and R. Kohn. This work was carried out during MO's stay at the Max Planck Institute for Mathematics in the Sciences of Leipzig, Germany, under the auspices of the Humboldt Foundation. MO gratefully acknowledges the financial support provided by the Foundation and the hospitality extended by the Institute. SM was partially supported by the Deutsche Forschungsgemeinschaft DFG through SPP 1095 "Analysis, modelling, and simulation of multiscale problems." We would also like to thank the referees for their helpful suggestions.Additional details
- Eprint ID
- 83522
- Resolver ID
- CaltechAUTHORS:20171128-113838315
- Alexander von Humboldt Foundation
- SPP 1095
- Deutsche Forschungsgemeinschaft (DFG)
- Created
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2017-11-29Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Caltech groups
- GALCIT