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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| Author: | Bernd SchmidtGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-22066 |
| Frontdoor URL | https://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): |  Deutsches Urheberrecht |
