A convergent scheme for Hamilton-Jacobi equations on a junction: application to traffic (Q2260880)

The authors propose a finite difference method for the first-order Hamilton-Jacobi equation posed on a ``junction''. The junction is made of the finite number of half-lines with a unique common point. The authors prove the bounds of the numerical solutions under the discrete gradient and time derivative, and the convergence of numerical solutions to a viscosity solution. The presented method is applied to the traffic model, and considered as the Godunov method when the grid points are not on the ``junction''.