Communications in Mathematical Sciences

Volume 6 (2008)

Number 1

Stability of reconstruction schemes for scalar hyperbolic conservations laws

Pages: 57 – 70



Frédéric Lagoutière


We study the numerical approximation of scalar conservation laws in dimension 1 via general reconstruction schemes within the finite volume framework. We exhibit a new stability condition, derived from an analysis of the spatial convolutions of entropy solutions with characteristic functions of intervals. We then propose a criterion that ensures the existence of some numerical entropy fluxes. The consequence is the convergence of the approximate solution to the unique entropy solution of the considered equation.


hyperbolic equations; numerical schemes; reconstruction schemes; entropy schemes

2010 Mathematics Subject Classification

35L65, 65M12

Published 1 January 2008