On the Infinite Particle Limit in Lagrangian Dynamics and Convergence of Optimal Transportation Meshfree Methods

  • We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle trajectories. Also the convergence of stationary points of the action is established. Minimizers of the limiting functional and, more generally, limiting distributions of stationary points are investigated and shown to be concentrated on orbits of the Euler-Lagrange flow. We also consider time discretized systems. These results in particular provide a convergence analysis for optimal transportation meshfree methods for the approximation of particle flows by finite discrete Lagrangian dynamics.

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Metadaten
Author:Bernd SchmidtGND
URN:urn:nbn:de:bvb:384-opus4-22066
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/2206
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2013-01)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Release Date:2013/01/16
Tag:Lagrangian dynamics; optimal transportation meshfree methods; convergence analysis
GND-Keyword:Lagrange-Bewegungsgleichungen; Transportgleichung; Konvergenz; Gitterfreie Methode
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht