ERROR ESTIMATE OF A BIFIDELITY METHOD FOR KINETIC EQUATIONS WITH RANDOM PARAMETERS AND MULTIPLE SCALES
Irene M. Gamba, Shi Jin, Liu Liu · International Journal for Uncertainty Quantification · 2021
In this paper, we conduct uniform error estimates of the bifidelity method for multiscale kinetic equations. We take the Boltzmann and the linear transport equations as important examples, and discuss various choices of low-fidelity models for more general kinetic equations. 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.