带初始弱正则性的时间分数阶Navier-Stokes方程的数值分析

Numerical Analysis of the Time Fractional Navier-Stokes Equations with Weak Regular Solution

研究带有Caputo导数的二维时间分数阶Navier-Stokes方程的一种有效数值方法。考虑到时间分数阶偏微分方程的解在初始时刻往往具有弱正则性,故使用非一致网格上的L1方法离散时间分数阶导数,空间方向使用经典的Galerkin有限元方法逼近,得到全离散数值格式,并分析这个格式的稳定性和收敛性。

In this paper, derived has been an efficient numerical method for solving the two-dimensional Caputo-type Navier-Stokes equations. Considering the solution to the time-fractional partial differential equation tends to have weak regularity at the initial time, we discretize the time-fractional derivative by the L1 method on non-uniform meshes and the spatial derivative by the classical Galerkin finite element method. A fully discrete numerical scheme is obtained, with the stability and convergence of the scheme analyzed.