| Issue |
ESAIM: M2AN
Volume 55, Number 2, March-April 2021
|
|
|---|---|---|
| Page(s) | 689 - 711 | |
| DOI | https://doi.org/10.1051/m2an/2021006 | |
| Published online | 01 April 2021 | |
A non-local macroscopic model for traffic flow
Normandie Univ, INSA de Rouen Normandie, LMI (EA 3226 – FR CNRS 3335), 76000 Rouen, France, 685 Avenue de l’Université, 76801 St. Etienne du Rouvray Cedex, France
* Corresponding author: nicolas.forcadel@insa-rouen.fr
Received:
25
September
2020
Accepted:
26
January
2021
In this work, we propose a non-local Hamilton–Jacobi model for traffic flow and we prove the existence and uniqueness of the solution of this model. This model is justified as the limit of a rescaled microscopic model. We also propose a numerical scheme and we prove an estimate error between the continuous solution of this problem and the numerical one. Finally, we provide some numerical illustrations.
Mathematics Subject Classification: 76A30 / 35B27 / 35D40 / 35F21
Key words: Traffic flow / macroscopic models / non-local model / homogenization / viscosity solutions / Hamilton–Jacobi equations
© The authors. Published by EDP Sciences, SMAI 2021
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