On wavewise entropy inequalities for high-resolution schemes. I: The semidiscrete case

@article{Yang1996OnWE,
  title={On wavewise entropy inequalities for high-resolution schemes. I: The semidiscrete case},
  author={Huanan Yang},
  journal={Math. Comput.},
  year={1996},
  volume={65},
  pages={45-67}
}
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

Publications referenced by this paper.
Showing 1-10 of 27 references

Riemann solvers, the entropy condition and difference approximations

  • S. Osher
  • SIAM J. Numer. Anal
  • 1984
Highly Influential
18 Excerpts

The space BV and quasi-linear equations, Math

  • A. Vol′pert
  • USSR Sb
  • 1967
Highly Influential
5 Excerpts

Convenient total variation diminishing conditions for nonlinear difference schemes

  • E. Tadmor
  • SIAM J. Numer. Anal
  • 1988
Highly Influential
3 Excerpts

High resolution schemes and entropy condition

  • S. Osher, S. Chakravarthy
  • SIAM J. Numer. Anal
  • 1984
Highly Influential
4 Excerpts

Un exemple de méthode MUSCL satisfaisant toutes les inégalités d’entropie numériques

  • F. Bouchut, C. Bourdarias, B. Perthame
  • C.R. Acad. Sci. Paris, Sér. I. Math
  • 1993
Highly Influential
2 Excerpts

Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws

  • P K.
  • SIAM J. Numer. Anal
  • 1984
Highly Influential
3 Excerpts

An artificial compression method for ENO schemes: the slope modification method

  • H. Yang
  • J. Comput. Phys
  • 1990
1 Excerpt

Convergence of MUSCL type methods for scalar conservation laws

  • P. Souganidis
  • C . R . Acad . Sci . Paris .
  • 1990

Souganidis, Convergence of MUSCL type methods for scalar conservation laws, C

  • P. P. Lions
  • R. Acad. Sci. Paris. Sér. I Math
  • 1990
1 Excerpt

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