An Instability of the Godunov Scheme

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dc.creatorBressan, Alberto
dc.creatorJenssen, Helge Kristian
dc.creatorBaiti, Paolo
dc.date2005-02-07
dc.date.accessioned2026-07-07T05:16:45Z
dc.date.available2026-07-07T05:16:45Z
dc.descriptionWe 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.
dc.description40 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0502125
dc.identifierhttp://arxiv.org/abs/math/0502125
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74101
dc.subjectAnalysis of PDEs
dc.titleAn Instability of the Godunov Scheme
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