Li Xiaocui, Yang Xiaoyuan
1School of Science, Beijing University of Chemical Technology, Beijing, P.R. China.
2LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, P.R. China.
J Inequal Appl. 2018;2018(1):284. doi: 10.1186/s13660-018-1880-y. Epub 2018 Oct 19.
Based on the Itô's isometry and the properties of the solution operator defined by the Mittag-Leffler function, this paper gives a detailed numerical analysis of the finite element method for fractional stochastic Navier-Stokes equations driven by white noise. The discretization in space is derived by the finite element method and the time discretization is obtained by the backward Euler scheme. The noise is approximated by using the generalized -projection operator. Optimal strong convergence error estimates in the -norm are obtained.
基于伊藤等距性以及由米塔格 - 莱夫勒函数定义的解算子的性质，本文对由白噪声驱动的分数阶随机纳维 - 斯托克斯方程的有限元方法进行了详细的数值分析。空间离散化通过有限元方法得到，时间离散化通过向后欧拉格式获得。噪声通过使用广义投影算子进行近似。得到了(L^2)范数下的最优强收敛误差估计。
