| Title | An instability of the Godunov scheme |
| Publication Type | Journal Article |
| Year of Publication | 2006 |
| Authors | Bressan, A, Jenssen, HK, Baiti, P |
| Journal | Comm. Pure Appl. Math. 59 (2006) 1604-1638 |
| 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. |
| URL | http://hdl.handle.net/1963/2183 |
| DOI | 10.1002/cpa.20141 |
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