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Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2012

Error estimate for Godunov approximation of locally constrained conservation laws

Clément Cancès
Nicolas Seguin

Résumé

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.
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Dates et versions

hal-00599581 , version 1 (10-06-2011)
hal-00599581 , version 2 (01-03-2012)

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Clément Cancès, Nicolas Seguin. Error estimate for Godunov approximation of locally constrained conservation laws. SIAM Journal on Numerical Analysis, 2012, 50 (6), pp.3036--3060. ⟨10.1137/110836912⟩. ⟨hal-00599581v2⟩
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