Abstract

We present techniques for the analysis and numerical analysis of non-local non-linear PDEs. We apply these techniques to an equation derived from the modelling of traffic flow. We introduce a macroscopic model in the form of a Hamilton--Jacobi equation with a junction condition. More precisely, the goal of this work is to obtain the numerical homogenization of a non-local PDE deriving from a first order discrete model for traffic flow that simulates the presence of a local perturbation. Previously we showed that the solution of the discrete microscopic model converges to the (unique) solution of a Hamilton--Jacobi equation posed on a network and with a junction condition (it can be seen as a flux limiter that keeps the memory of the local perturbation). The goal of this article is to provide a numerical scheme able to obtain an approximation of this flux-limiter. We prove the convergence of this scheme and we give some numerical results.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.