论文标题
具有加性噪声的随机Navier-Stokes方程的完全离散的混合有限元近似值的高矩和路径误差估计值
High moment and pathwise error estimates for fully discrete mixed finite element approximattions of stochastic Navier-Stokes equations with additive noise
论文作者
论文摘要
本文涉及具有一般添加剂噪声的随机Navier-Stokes方程的完全离散的混合有限元近似值的高力矩和路径误差估计。分别用于时间和空间离散化，分别采用了隐式Euler-Maruyama方案和标准混合有限元方法。速度的高矩误差估计值和强$ l^2 $中的时间避免压力近似值，并且获得了能量规范，通过使用Kolmogorov定理得出路径误差估计。与他们的derterminisis同行不同，空间错误常数按$ o（k^{ - \ frac12}）$的顺序增长，其中$ k $表示时间步长。还提供了数值实验来验证误差估计及其清晰度。
This paper is concerned with high moment and pathwise error estimates for fully discrete mixed finite element approximattions of stochastic Navier-Stokes equations with general additive noise. The implicit Euler-Maruyama scheme and standard mixed finite element methods are employed respectively for the time and space discretizations. High moment error estimates for both velocity and a time-avraged pressure approximations in strong $L^2$ and energy norms are obtained, pathwise error estimates are derived by using the Kolmogorov Theorem. Unlike their derterministic counterparts, the spatial error constants grow in the order of $O(k^{-\frac12})$, where $k$ denotes time step size. Numerical experiments are also provided to validate the error estimates and their sharpness.
