I just uploaded on HAL and arxiv a new preprint written with Marwa Koumaiha (Univ. Paris-Est Créteil and Lebanese University) about Error estimates for finite difference schemes associated with Hamilton-Jacobi equations on a junction.
Abstract: This paper is concerned with monotone (time-explicit) finite difference schemes associated with first order Hamilton-Jacobi equations posed on a junction. They extend the schemes recently introduced by Costeseque, Lebacque and Monneau (2013) to general junction conditions. On one hand, we prove the convergence of the numerical solution towards the weak (viscosity) solution of the Hamilton-Jacobi equation as the mesh size tends to zero for general junction conditions. On the other hand, we derive error estimates of order (∆x) 1 3 in L ∞ loc for junction conditions of optimal-control type.