Lagrangian-Antidiffusive Remap schemes for non-local multi-class traffic flow models

International audienceThis paper focuses on the numerical approximation of the solutions of a class of non-local systems in one space dimension, arising in traffic modeling. We propose alternative simple schemes by splitting the non-local conservation laws into two different equations, namely, the Lagrangian and the remap steps. We provide some properties and estimates recovered by approximating the problem with the L-AR scheme, and we prove the convergence to weak solutions in the scalar case. Finally, we show some numerical simulations illustrating the efficiency of the L-AR schemes in comparison with classical first and second order numerical schemes

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

30 pagesInternational audienceIn this paper, we consider first order Hamilton-Jacobi (HJ) equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. For this continuous HJ problem, we propose a finite difference scheme and prove two main results. As a first result, we show bounds on the discrete gradient and time derivative of the numerical solution. Our second result is the convergence (for a subsequence) of the numerical solution towards a viscosity solution of the continuous HJ problem, as the mesh size goes to zero. When the solution of the continuous HJ problem is unique, we recover the full convergence of the numerical solution. We apply this scheme to compute the densities of cars for a traffic model. We recover the well-known Godunov scheme outside the junction point and we give a numerical illustration

Lagrangian-Antidiffusive Remap schemes for non-local multi-class traffic flow models

International audienceThis paper focuses on the numerical approximation of the solutions of a class of non-local systems in one space dimension, arising in traffic modeling. We propose alternative simple schemes by splitting the non-local conservation laws into two different equations, namely, the Lagrangian and the remap steps. We provide some properties and estimates recovered by approximating the problem with the L-AR scheme, and we prove the convergence to weak solutions in the scalar case. Finally, we show some numerical simulations illustrating the efficiency of the L-AR schemes in comparison with classical first and second order numerical schemes

Value iteration convergence of ε-monotone schemes for stationary Hamilton-Jacobi equations

International audienceWe present an abstract convergence result for the xed point approximation of stationary Hamilton{Jacobi equations. The basic assumptions on the discrete operator are invariance with respect to the addition of constants, "-monotonicity and consistency. The result can be applied to various high-order approximation schemes which are illustrated in the paper. Several applications to Hamilton{Jacobi equations and numerical tests are presented