| Abstract: |
| We first extend the prodigm of asymptotic-preserving schemes to the random kinetic equations, and show how it can be constructed in the setting of the stochastic Galerkin approximations. We then extend the hypocoercivity theory, developed for deterministic kinetic equations, to the random case, and establish in the random space regularity, long-time sensitivity analysis, and uniform (in Knudsen number) spectral convergence of the stochastic Galerkin methods, for general linear and nonlinear random kinetic equations in various asymptotic-including the diffusion, incompressible Navier-Stokes, high-field, and acoustic regimes. |
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