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 in .

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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

Email:
makr@math.uch.gr

DOI:
https://doi.org/10.1090/S0025-5718-00-01188-1

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