We present new error estimates for the finite volume and finite difference methods applied to the compressible Navier–Stokes equations. The main innovative ingredients of the improved error estimates are a refined consistency analysis combined with a continuous version of the relative energy inequality. Consequently, we obtain better convergence rates than those available in the literature so far. Moreover, the error estimates hold in the whole physically relevant range of the adiabatic coefficient.

中文翻译：

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改进的有限体积误差估计和可压缩 Navier-Stokes 系统的 MAC 方案

我们提出了适用于可压缩 Navier-Stokes 方程的有限体积和有限差分方法的新误差估计。改进误差估计的主要创新成分是改进的一致性分析与相对能量不平等的连续版本相结合。因此，我们获得了比迄今为止文献中可用的收敛率更好的收敛率。此外，误差估计适用于绝热系数的整个物理相关范围。