Error estimate for Godunov approximation of locally constrained conservation laws

Clément Cancès (1) , Nicolas Seguin (1)

1 LJLL - Laboratoire Jacques-Louis Lions

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 $BV$-estimate, and make use of it to provide an error estimate of optimal order $h^{1/2}$ for the Godunov approximation of the problem. Numerical illustrations are then provided to illustrate the optimality of the result.

Mots clés: error estimate

Mots clés: Locally constrained scalar conservation laws; monotone finite volume scheme; BV-estimate; error estimate.

Domaines: Equations aux dérivées partielles [math.AP]

Clément Cancès, Nicolas Seguin. Error estimate for Godunov approximation of locally constrained conservation laws. 2011. ⟨hal-00599581v1⟩