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The entropy dissipation by numerical viscosity in nonlinear conservative difference schemes

  • Numerical Analysis
  • Conference paper
  • First Online:
Nonlinear Hyperbolic Problems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1270))

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Abstract

We study the question of entropy stability for discrete approximations to hyperbolic systems of conservation laws. We quantify the amount of numerical viscosity present in such schemes, and relate it to their entropy stability by means of comparison. To this end, two main ingredients are used: the entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. We then show that conservative schemes are entropy stable, if they contain more numerical viscosity than the above mentioned entropy conservative ones.

Research was supported in part by NASA Contract Nos. NAS1-17070 and NAS1-18107 while the author was in residence at ICASE, NASA Langley Research Center, Hampton, VA 23665. Additional support was provided by NSF Grant No. DMS85-03294 and ARO Grant No. DAAG29-85-K-0190 while in residence at the University of California, Los Angeles, CA 90024. The author is a Bat-Sheva Foundation Fellow.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Italy

    Eitan Tadmor

  2. Institute for Computer Applications in Science and Engineering, Italy

    Eitan Tadmor

Authors
  1. Eitan Tadmor
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Editor information

Claude Carasso Denis Serre Pierre-Arnaud Raviart

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© 1987 Springer-Verlag

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Tadmor, E. (1987). The entropy dissipation by numerical viscosity in nonlinear conservative difference schemes. In: Carasso, C., Serre, D., Raviart, PA. (eds) Nonlinear Hyperbolic Problems. Lecture Notes in Mathematics, vol 1270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078317

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  • DOI: https://doi.org/10.1007/BFb0078317

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18200-9

  • Online ISBN: 978-3-540-47805-8

  • eBook Packages: Springer Book Archive

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