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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On Wavewise Entropy Inequalities for
High-Resolution Schemes. I: The Semidiscrete Case


Author: Huanan Yang
Journal: Math. Comp. 65 (1996), 45-67
MSC (1991): Primary 65M60, 65M12, 35L65
Supplement: Additional information related to this article.
MathSciNet review: 1320900
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Abstract | References | Similar Articles | Additional Information

Abstract: We develop a new approach, the method of wavewise entropy inequalities for the numerical analysis of hyperbolic conservation laws. The method is based on a new extremum tracking theory and Volpert's theory of BV solutions. The method yields a sharp convergence criterion which is used to prove the convergence of generalized MUSCL schemes and a class of schemes using flux limiters previously discussed in 1984 by Sweby.


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Additional Information

Huanan Yang
Affiliation: Department of Mathematics\ Kansas State University\ Manhattan, Kansas 66506
Email: hyang@math.ksu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00668-0
PII: S 0025-5718(96)00668-0
Keywords: Conservation law, MUSCL schemes, schemes using flux limiters, entropy condition, convergence
Received by editor(s): December 20, 1993
Received by editor(s) in revised form: September 13, 1994, and January 30, 1995
Article copyright: © Copyright 1996 American Mathematical Society