We propose and study a fully discrete finite volume scheme for the Vlasov-Fokker-Planck equation written as an hyperbolic system using Hermite polynomials in velocity. This approach naturally preserves the stationary solution and the weighted L 2 relative entropy. Then, we adapt the arguments developed in [12] based the hypocoercivity method to get quantitative estimates on the convergence to equilibrium of the discrete solution. Finally, we prove that in the diffusive limit, the scheme is asymptotic preserving with respect to both the time variable and the scaling parameter at play.

翻译：我们建议并研究一个完全独立的Vlasov-Fokker-Planck 等式数量有限计划,该计划是用速速的Hermite多元分子制的双曲系统。 这种方法自然保留固定式溶液和加权的L 2 相对酶。 然后, 我们调整以[12] 为基础的低吸附法开发的参数, 以获得关于离散溶方的趋同与平衡的定量估计。 最后, 我们证明, 在 diffusive 限制中, 计划对时间变量和正在运行的缩放参数都保持不严谨。