High Moment and Pathwise Error Estimates for Fully Discrete Mixed Finite Element Approximations of Stochastic Navier-Stokes Equations with Additive Noise
Year: 2024
Author: Xiaobing Feng, Liet Vo
Communications in Computational Physics, Vol. 36 (2024), Iss. 3 : pp. 821–849
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0234
Communications in Computational Physics, Vol. 36 (2024), Iss. 3 : pp. 821–849
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Stochastic Navier-Stokes equations additive noise Wiener process Itô stochastic integral mixed finite element methods inf-sup condition high moment and pathwise error estimates.