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Mathematics of Computation

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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

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