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：本文证明了守恒律方程组的保守型有限差分格式中，谱稳定定常离散激波解的线性轨道稳定性。证明依赖于对这些离散激波解相关格林函数的逐点渐近行为的精确描述，改进了Lafitte-Godillon [God03] 的结果。该稳定性结果的主要创新在于适用于一类可引入人工可能高阶粘性的广泛差分格式。该结果是在严格的谱假设下获得的，而不是通过对激波振幅施加小量假设。