Error estimates for finite difference schemes associated with Hamilton-Jacobi equations on a junction

39 pages. In the initial version, the proof of the error estimate only works for Hamiltonians with the same minimum with no flux limiter. In the revised version, we can handle general quasi-convex Hamiltonians and flux limiters. We also provide numerical simulations.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 the one hand, we prove the convergence of the numerical solution towards the viscosity solution of the Hamilton-Jacobi equation as the mesh size tends to zero for general junction conditions. On the other hand, we derive optimal error estimates of order $(\Delta x)^{\frac{1}{2}}$ in $L_{loc}^{\infty}$ for junction conditions of optimal-control type at least if the flux is "strictly limited"