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Mathematics of Computation

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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
Published electronically: March 3, 2000
MathSciNet review: 1681104
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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

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

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