We prove the linear orbital stability of spectrally stable stationary discrete shock profiles for conservative finite difference schemes applied to systems of conservation laws. The proof relies on a precise description of the pointwise asymptotic behavior of the Green's function associated with those discrete shock profiles, improving on the result of Godillon [God03]. The main novelty of this stability result is that it applies for a fairly large family of schemes that introduce some artificial viscosity and most importantly, that we do not impose any weakness assumption on the shock.

翻译：我们证明了守恒律系统在保守有限差分格式下，谱稳定的驻定离散激波剖面的线性轨道稳定性。证明依赖于对这些离散激波剖面相关格林函数逐点渐近行为的精确描述，改进了Godillon[God03]的结果。这一稳定性结果的主要创新在于，它适用于引入人工粘性的一大类格式，且最关键的是，我们未对激波施加任何弱性假设。