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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
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: http://dx.doi.org/10.1090/S0025-5718-06-01863-1
PII: S 0025-5718(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.