In this seminar we present a numerical scheme for the approximation of viscosity solutions of a class of Hamilton-Jacobi equations on ramified domains. The scheme is explicit and stable under appropriate technical conditions. We show a convergence theorem and a priori estimates of numerical error. The theoretical results are confirmed by specific tests. To conclude, we apply the scheme to the simulation of vehicular traffic problems. Work developed in collaboration with E. Carlini (Sapienza, Rome) and N. Forcadel (INSA, Rouen).
