Müller, S. and Ortiz, M. (2004) On the Γ-convergence of discrete dynamics and variational integrators. Journal of Nonlinear Science, 14 (3). pp. 279-296. ISSN 0938-8974. doi:10.1007/BF02666023. https://resolver.caltech.edu/CaltechAUTHORS:20171128-113838315
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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 {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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| 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. | ||||||||||||
| Group: | GALCIT | ||||||||||||
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| Issue or Number: | 3 | ||||||||||||
| DOI: | 10.1007/BF02666023 | ||||||||||||
| Record Number: | CaltechAUTHORS:20171128-113838315 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171128-113838315 | ||||||||||||
| Official Citation: | Müller, S. & Ortiz, M. J Nonlinear Sci (2004) 14: 279. https://doi.org/10.1007/BF02666023 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 83522 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Lydia Suarez | ||||||||||||
| Deposited On: | 29 Nov 2017 00:24 | ||||||||||||
| Last Modified: | 15 Nov 2021 20:11 |
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