On wavewise entropy inequalities for high-resolution schemes. I: The semidiscrete case
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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 Vol′pert’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.References
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Additional Information
- Huanan Yang
- Affiliation: Department of Mathematics Kansas State University Manhattan, Kansas 66506
- Email: hyang@math.ksu.edu
- Received by editor(s): December 20, 1993
- Received by editor(s) in revised form: September 13, 1994, and January 30, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 45-67
- MSC (1991): Primary 65M60, 65M12, 35L65
- DOI: https://doi.org/10.1090/S0025-5718-96-00668-0
- MathSciNet review: 1320900