TY - JOUR
T1 - High Moment and Pathwise Error Estimates for Fully Discrete Mixed Finite Element Approximations of Stochastic Navier-Stokes Equations with Additive Noise
AU - Feng , Xiaobing
AU - Vo , Liet
JO - Communications in Computational Physics
VL - 3
SP - 821
EP - 849
PY - 2024
DA - 2024/10
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2023-0234
UR - https://global-sci.org/intro/article_detail/cicp/23459.html
KW - Stochastic Navier-Stokes equations, additive noise, Wiener process, Itô stochastic integral, mixed finite element methods, inf-sup condition, high moment, and pathwise error estimates.
AB - <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>