Finite volume relaxation schemes for multidimensional conservation laws
Authors:
Theodoros Katsaounis and Charalambos Makridakis
Journal:
Math. Comp. 70 (2001), 533-553
MSC (2000):
Primary 65M12, 65M15; Secondary 65L06
DOI:
https://doi.org/10.1090/S0025-5718-00-01188-1
Published electronically:
March 3, 2000
MathSciNet review:
1681104
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Abstract | References | Similar Articles | Additional Information
Abstract: We consider finite volume relaxation schemes for multidimensional scalar conservation laws. These schemes are constructed by appropriate discretization of a relaxation system and it is shown to converge to the entropy solution of the conservation law with a rate of $h^{1/4}$ in $L^{\infty }([0, T] , L^{1} _\mathrm {loc}({\mathbb {R}} ^{d} ))$.
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Additional Information
Theodoros Katsaounis
Affiliation:
Ecole Normale Supérieure, Département de Mathématique et d’Informatique, 45 rue d’Ulm, 75230 Paris Cedex 05, France
Email:
Theodoros.Katsaounis@ens.fr, thodoros@math.uch.gr
Charalambos Makridakis
Affiliation:
Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, and Institute of Applied and Computational Mathematics, FORTH, 711 10 Heraklion, Crete, Greece
MR Author ID:
289627
Email:
makr@math.uch.gr
Received by editor(s):
October 31, 1997
Received by editor(s) in revised form:
September 23, 1998, November 20, 1998, and March 9, 1999
Published electronically:
March 3, 2000
Article copyright:
© Copyright 2000
American Mathematical Society
