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.

翻译：我们提出了适用于压缩的纳维埃-斯托克斯方程式的有限数量和有限差异方法的新误差估计。改进误差估计的主要创新要素是完善的一致性分析,加上对相对能源不平等的连续版本。因此,我们比文献中迄今的趋同率提高了。此外,误差估计与对数系数的整个物理范围相关。