In this paper, we conduct uniform error estimates of the bi-fidelity method for multi-scale kinetic equations. We take the Boltzmann and the linear transport equations as important examples. The main analytic tool is the hypocoercivity analysis for kinetic equations, considering solutions in a perturbative setting close to the global equilibrium. This allows us to obtain the error estimates in both kinetic and hydrodynamic regimes.

翻译：在本文中,我们对多尺度动能方程式的双性畸形方法进行统一的误差估计。我们把布尔兹曼和线性传输方程式作为重要的例子。主要的分析工具是动能方程式的低调分析,在接近全球平衡的扰动环境中考虑解决方案。这使我们能够在动能和流体动力系统中获得误差估计。