A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

Author:
Volker Elling

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

Published electronically:
June 19, 2006

MathSciNet review:
2240632

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Abstract | References | Similar Articles | Additional Information

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

DOI:
https://doi.org/10.1090/S0025-5718-06-01863-1

Keywords:
Conservation law,
well posedness,
entropy solution,
Riemann problem,
shock,
contact discontinuity,
compressible Euler equations,
entropy/entropy flux pair

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.

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.