  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".
