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March 2008 Stability of reconstruction schemes for scalar hyperbolic conservations laws
Frédéric Lagoutière
Commun. Math. Sci. 6(1): 57-70 (March 2008).


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.


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Frédéric Lagoutière. "Stability of reconstruction schemes for scalar hyperbolic conservations laws." Commun. Math. Sci. 6 (1) 57 - 70, March 2008.


Published: March 2008
First available in Project Euclid: 7 March 2008

zbMATH: 1140.35325
MathSciNet: MR2397997

Primary: 35L65 , 65M12

Keywords: entropy schemes , Hyperbolic equations , Numerical schemes , reconstruction schemes

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 1 • March 2008
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