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In this paper, we conduct uniform error estimates of the bi-fidelity methodfor multi-scale kinetic equations. We take the Boltzmann and the lineartransport equations as important examples. The main analytic tool is thehypocoercivity analysis for kinetic equations, considering solutions in aperturbative setting close to the global equilibrium. This allows us to obtainthe error estimates in both kinetic and hydrodynamic regimes.

Error estimate of a bi-fidelity method for kinetic equations with random parameters and multiple scales