Communications in Mathematical Sciences

Stability of reconstruction schemes for scalar hyperbolic conservations laws

Frédéric Lagoutière

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Abstract

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

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

Dates
First available in Project Euclid: 7 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.cms/1204905777

Mathematical Reviews number (MathSciNet)
MR2397997

Zentralblatt MATH identifier
1140.35325

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

Keywords
hyperbolic equations numerical schemes reconstruction schemes entropy schemes

Citation

Lagoutière, Frédéric. Stability of reconstruction schemes for scalar hyperbolic conservations laws. Commun. Math. Sci. 6 (2008), no. 1, 57--70. https://projecteuclid.org/euclid.cms/1204905777


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