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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence
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Math. Comp. 75 (2006), 1721-1733 Request permission

Abstract:

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.
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Additional Information
  • Volker Elling
  • Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
  • Email: velling@stanfordalumni.org
  • Received by editor(s): November 7, 2004
  • Received by editor(s) in revised form: May 5, 2005
  • Published electronically: June 19, 2006
  • Additional Notes: This material is based upon work supported by an SAP/Stanford Graduate Fellowship and by the National Science Foundation under Grant no. DMS 0104019. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 75 (2006), 1721-1733
  • MSC (2000): Primary 35L65, 35L67, 76L05, 76H05, 76N10
  • DOI: https://doi.org/10.1090/S0025-5718-06-01863-1
  • MathSciNet review: 2240632