(untitled) (Communications in Computational Physics, 2024)
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 O(k^-12 ), where k denotes time step size. Numerical experiments are also provided to validate the error estimates and their sharpness.