论文标题
在动力学方程的离散框架中
On a discrete framework of hypocoercivity for kinetic equations
论文作者
论文摘要
我们建议并研究使用速度中的Hermite多项式编写为双曲线系统的Vlasov-Fokker-Planck方程完全分散的有限体积方案。这种方法自然保留了固定溶液和加权L 2相对熵。然后，我们调整基于[12]中开发的参数低核心方法，以获取对离散溶液平衡的收敛性估计。最后，我们证明，在扩散极限中，该方案是渐近保存的时间变量和尺度参数。
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.
