Error estimate for Godunov approximation of locally constrained conservation laws

International audience; We consider a model of traffic flow with unilateral constraint on the flux introduced by {\sc R. M. Colombo} and {\sc P. Goatin} (J. Differ. Equ. 234(2):654--675, 2007), for which the convergence of numerical approximation using monotone finite volume schemes has been performed by B. {\sc Andreianov} {\em et al.}~(Numer. Math. 115:609--645, 2010). We derive for this problem some new ${\rm BV}$-estimate, and make use of it to provide an error estimate for the Godunov approximation of the problem of order $h^{1/3}$ that is improved into the optimal order $h^{1/2}$ under a reasonable assumption. Numerical experiments are then provided to illustrate the optimality of the result.