Communications in Mathematical Sciences

Stability of reconstruction schemes for scalar hyperbolic conservations laws

Frédéric Lagoutière

Full-text: Open access


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.

Article information

Commun. Math. Sci., Volume 6, Number 1 (2008), 57-70.

First available in Project Euclid: 7 March 2008

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L65: Conservation laws 65M12: Stability and convergence of numerical methods

hyperbolic equations numerical schemes reconstruction schemes entropy schemes


Lagoutière, Frédéric. Stability of reconstruction schemes for scalar hyperbolic conservations laws. Commun. Math. Sci. 6 (2008), no. 1, 57--70.

Export citation