[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | All | Home ]

Preprint 2012-022

Error estimate for Godunov approximation of locally constrained conservation laws

Clément Cancès and Nicolas Seguin

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.