@Article{CiCP-36-821,
author = {Feng , Xiaobing and Vo , Liet},
title = {High Moment and Pathwise Error Estimates for Fully Discrete Mixed Finite Element Approximations of Stochastic Navier-Stokes Equations with Additive Noise},
journal = {Communications in Computational Physics},
year = {2024},
volume = {36},
number = {3},
pages = {821--849},
abstract = {<p style="text-align: justify;">This paper is concerned with high moment and pathwise error estimates for
fully discrete mixed finite element approximations 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 time-averaged pressure approximations in strong $L^2$ and energy norms are obtained, pathwise error estimates are derived by using the Kolmogorov Theorem. Unlike their deterministic
counterparts, the spatial error constants grow in the order of $\mathcal{O}(k^{-\frac{1}{2}} ),$ where $k$ denotes
time step size. Numerical experiments are also provided to validate the error estimates
and their sharpness.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0234},
url = {http://global-sci.org/intro/article_detail/cicp/23459.html}
}