An instability of the Godunov scheme
An instability of the Godunov scheme
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Godunov 方案的不稳定性
DOI：
10.1002/cpa.20141
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发表时间：
2005
影响因子：
3
通讯作者：
P. Baiti
中科院分区：
文献类型：
--
作者：
A. Bressan;H. Jenssen;P. Baiti
我们构造了一个2 × 2严格双曲守恒律组的解，证明了Goddom格式[13]可以产生任意大的振荡量。当电击的速度接近理性时，就会发生这种情况，从而引起电网的共振。与Glimm格式或消失粘性方法不同，对于守恒律系统，我们的反例表明，对于有限差分格式，通常没有先验BV界或L1稳定性估计是有效的。© 2006 Wiley Periodicals，Inc.
We construct a solution to a 2 × 2 strictly hyperbolic system of conservation laws, showing that the Godunov scheme [13] 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 L1‐stability estimates can in general be valid for finite difference schemes. © 2006 Wiley Periodicals, Inc.