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# Error estimate for Godunov approximation of locally constrained conservation laws

Abstract: We consider a model of traffic flow with unilateral constraint on the flux introduced by R. M. Colombo and P. Goatin [14], for which the convergence of numerical approximation using monotone finite volume schemes has been performed by B. Andreianov et al. [4]. We derive for this problem some new 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.

References
[4] B. Andreianov, P. Goatin, and N. Seguin, Finite volume schemes for locally constrained conservation laws, Numer. Math., 115 (2010), pp. 609–645. With supplementary material available online.
[14] R. M. Colombo and P. Goatin, A well posed conservation law with a variable unilateral constraint, J. Differential Equations, 234 (2007), pp. 654–675.
Paper:
Available as PDF (324 Kbytes).
Author(s):
Clément Cancès,
Nicolas Seguin,
Submitted by:
; 2012-09-19.