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Error estimate of a bi-fidelity method for kinetic equations with random parameters and multiple scales (1910.09080v2)
Published 20 Oct 2019 in math.NA, cs.NA, math-ph, and math.MP
Abstract: 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.