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 an accurate description of the pointwise asymptotic behavior of the Green's function associated with those discrete shock profiles, improving on the result of Lafitte-Godillon [God03]. The main novelty of this stability result is that it applies to a fairly large family of schemes that introduce some artificial possibly high-order viscosity. The result is obtained under a sharp spectral assumption rather than by imposing a smallness assumption on the shock amplitude.

翻译：我们证明了应用于守恒律方程组的保守有限差分格式中谱稳定的稳态离散激波剖面的线性轨道稳定性。该证明依赖于对这些离散激波剖面相关的格林函数逐点渐近行为的精确描述，改进了Lafitte-Godillon [God03]的结果。此稳定性结果的主要新颖之处在于它适用于引入某种人工（可能为高阶）粘性的相当广泛的格式族。该结果是在尖锐的谱假设下获得的，而非通过对激波振幅施加小性假设。