Numerical Analysis and Scientific Computing Seminar | Adriano Festa, A semi-Lagrangian scheme for Hamilton-Jacobi equations on networks and its application to vehicular traffic models

MC 5501 and Zoom (Please contact rgugliel@uwaterloo.ca for meeting link) 

Speaker

Adriano Festa, Associate Professor, Department of Mathematical Sciences at the Technical university of Turin

Title

A semi-Lagrangian scheme for Hamilton-Jacobi equations on networks and its application to vehicular traffic models

Abstract

We present a semi-Lagrangian scheme for the approximation of a class of Hamilton-Jacobi-Bellman (HJB) equations on networks. The scheme is explicit, consistent, and stable for large time steps. We prove a convergence result and two error estimates. For an HJB equation with space-independent Hamiltonian, we obtain a first order error estimate. In the general case, we provide, under a hyperbolic CFL condition, a convergence estimate of order one half. The theoretical results are discussed and validated in a numerical tests section, where we show some application of the techniques proposed to the approximation of traffic flows.