论文标题
Fokker-Planck-Landau方程的保守光谱法的收敛和误差估计值
Convergence and Error Estimates for the Conservative Spectral Method for Fokker-Planck-Landau Equations
论文作者
论文摘要
对于近似与硬势相关的半差异光谱法（FPL）方程，对半差异版本的保守光谱方法的严格估计值进行了严格得出。分析包括表明，半混凝土问题具有有界矩的独特解决方案。此外，在某些条件下，此类解决方案的衍生物在任何订单上也保持在全球时间的限制。这些估计值与光谱投影的控制相结合，足以获得分析溶液和融合到平衡状态的误差估计。应该注意的是，这是第一次为任何数值方法产生误差估计，该数值方法近似于与任何电势范围相关的FPL方程。
Error estimates are rigorously derived for a semi-discrete version of a conservative spectral method for approximating the space-homogeneous Fokker-Planck-Landau (FPL) equation associated to hard potentials. The analysis included shows that the semi-discrete problem has a unique solution with bounded moments. In addition, the derivatives of such a solution up to any order also remain bounded in $L^2$ spaces globally time, under certain conditions. These estimates, combined with control of the spectral projection, are enough to obtain error estimates to the analytical solution and convergence to equilibrium states. It should be noted that this is the first time that an error estimate has been produced for any numerical method which approximates FPL equations associated to any range of potentials.
