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Convergence of Generalized Muscl Schemes

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Upwind and High-Resolution Schemes

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Abstract

Semidiscrete generalizations of the second order extension of Godunov’s scheme, known as the MUSCL scheme, are constructed, starting with any three point “E” scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.

Received by the editors February 14, 1984. The research of this author was supported by the National Science Foundation under grant MCS 82-00788, the Army Research Office under grant DAAG 29-82-k-0090, and the National Aeronautics and Space Administration under grant NAG 1-270. Part of the research was carried out while the author was a visitor at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, Virginia, which is operated under NASA contract NASI-17070.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at Los Angeles, Los Angeles, California, 90024, USA

    Stanley Osher

Authors
  1. Stanley Osher
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Editor information

Editors and Affiliations

  1. Program in Computational Science & Engineering, Florida State University, Tallahassee, FL, 32306-3075, USA

    M. Yousuff Hussaini

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109-2118, USA

    Bram van Leer

  3. ICASE, NASA Langley Research Center, Mail Stop 132C, Hampton, VA, 23681-0001, USA

    John Van Rosendale

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© 1997 Springer-Verlag Berlin Heidelberg

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Osher, S. (1997). Convergence of Generalized Muscl Schemes. In: Hussaini, M.Y., van Leer, B., Van Rosendale, J. (eds) Upwind and High-Resolution Schemes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60543-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-60543-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64452-8

  • Online ISBN: 978-3-642-60543-7

  • eBook Packages: Springer Book Archive

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