A semi-Lagrangian scheme for Hamilton-Jacobi equations on networks with application to traffic flow models

Abstract

We present a semi-Lagrangian scheme for the approximation of a class of Hamilton-Jacobi-Bellman equations on networks. The scheme is explicit and stable under some technical conditions. We prove a convergence theorem and some error estimates. Additionally, the theoretical results are validated by numerical tests. Finally, we apply the scheme to simulate traffic flows modeling problems.

References in corpus (2)

• Multiscale modeling of granular flows with application to crowd dynamics
• Error estimates for finite difference schemes associated with Hamilton-Jacobi equations on a junction