@article {2006,
title = {An instability of the Godunov scheme},
journal = {Comm. Pure Appl. Math. 59 (2006) 1604-1638},
number = {arXiv.org;math/0502125v1},
year = {2006},
abstract = {We construct a solution to a $2\\\\times 2$ 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 $L^1$ stability estimates can in general be valid for finite difference schemes.},
doi = {10.1002/cpa.20141},
url = {http://hdl.handle.net/1963/2183},
author = {Alberto Bressan and Helge Kristian Jenssen and Paolo Baiti}
}