TY - JOUR
T1 - An instability of the Godunov scheme
JF - Comm. Pure Appl. Math. 59 (2006) 1604-1638
Y1 - 2006
A1 - Alberto Bressan
A1 - Helge Kristian Jenssen
A1 - Paolo Baiti
AB - 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.
UR - http://hdl.handle.net/1963/2183
U1 - 2061
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -