An Instability of the Godunov Scheme

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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.
40 pages, 3 figures

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Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/74101

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502125
 http://arxiv.org/abs/math/0502125

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arXiv