  We consider a mono-dimensional two-velocities scheme used to approximate the
solutions of a scalar hyperbolic conservative partial differential equation. We
prove the convergence of the discrete solution toward the unique entropy
solution by first estimating the supremum norm and the total variation of the
discrete solution, and second by constructing a discrete kinetic
entropy-entropy flux pair being given a continuous entropy-entropy flux pair of
the hyperbolic system. We finally illustrate our results with numerical
simulations of the advection equation and the Burgers equation.
