Preprint 2005-009

An Instability of the Godunov Scheme

Alberto Bressan, Helge Kristian Jenssen and Paolo Baiti

Abstract: We construct a solution to a 22 strictly hyperbolic system of conservation laws, showing that the Godunov scheme \cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or L1 stability estimates can in general be valid for finite difference schemes.



Paper:
Available as PDF (392 Kbytes), Postscript (1344 Kbytes) or gzipped PostScript (392 Kbytes; uncompress using gunzip).
Author(s):
Alberto Bressan, <bressan@math.psu.edu>
Helge Kristian Jenssen, <hkjensse@math.ncsu.edu>
Paolo Baiti, <baiti@dimi.uniud.it>
Publishing information:
Comments:
Submitted by:
<hkjensse@math.ncsu.edu> February 1 2005.


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