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Mathematics of Computation

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A MUSCL method satisfying all the numerical entropy inequalities

Authors: F. Bouchut, Ch. Bourdarias and B. Perthame
Journal: Math. Comp. 65 (1996), 1439-1461
MSC (1991): Primary 65M15, 35Q53, 35L65
MathSciNet review: 1348038
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Abstract: We consider here second-order finite volume methods for one-dimensional scalar conservation laws. We give a method to determine a slope reconstruction satisfying all the exact numerical entropy inequalities. It avoids inhomogeneous slope limitations and, at least, gives a convergence rate of $\Delta x^{1/2}$. It is obtained by a theory of second-order entropic projections involving values at the nodes of the grid and a variant of error estimates, which also gives new results for the first-order Engquist-Osher scheme.

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Additional Information

F. Bouchut
Affiliation: Département de Mathématiques, Université d’Orléans et CNRS, URA D1803, BP 6759, F45067 Orléans cedex 2, France

Ch. Bourdarias
Affiliation: Département de Mathématiques, Université de Chambéry, BP 104, F73011 Chambéry cedex, France

B. Perthame
Affiliation: Laboratoire d’Analyse Numérique, Université P. et M. Curie et CNRS UA 189, Tour 55/65, 5eme étage, 4, pl. Jussieu, F75252 Paris cedex 05, France

Keywords: Scalar conservation laws, MUSCL method, discrete entropy inequality, kinetic schemes, entropic slope reconstruction
Received by editor(s): August 4, 1994
Received by editor(s) in revised form: August 24, 1995
Article copyright: © Copyright 1996 American Mathematical Society