Entropy solutions of non-local scalar conservation laws with congestion via deterministic particle method
Analysis of PDEs
2021-08-12 v2 Numerical Analysis
Numerical Analysis
Abstract
We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general assumptions that the existing literature: the velocity fields are less regular (in particular the interaction force can have a discontinuity at the origin) with no prescribed attractive/repulsive regime and the mobility can have unbounded support. We complement our results with some numerical simulations, among which we show the applicability of the schemes to the multi-species setting.
Keywords
Cite
@article{arxiv.2107.10760,
title = {Entropy solutions of non-local scalar conservation laws with congestion via deterministic particle method},
author = {Emanuela Radici and Federico Stra},
journal= {arXiv preprint arXiv:2107.10760},
year = {2021}
}
Comments
41 pages, 18 figures