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

TL;DR

This paper introduces an explicit semi-Lagrangian numerical scheme for Hamilton-Jacobi equations on networks, with proven convergence and error estimates, validated through numerical tests and applied to traffic flow modeling.

Contribution

The paper develops a new semi-Lagrangian scheme for Hamilton-Jacobi equations on networks, including convergence proof and error analysis, with practical traffic flow applications.

Findings

Scheme is explicit and stable under certain conditions

Convergence theorem and error estimates are established

Numerical simulations successfully model traffic flow

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.