School of Mathematical & Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
6-2025
Abstract
This paper is concerned with high moment and pathwise error estimates for both velocity and pressure approximations of the Euler–Maruyama scheme for time discretization and its fully discrete mixed finite element discretization. Optimal rates of convergence are established for all pth moment errors for p ≥ 2 using a novel doubling of moments technique. The almost optimal rates of convergence are then obtained using Kolmogorov’s theorem based on the high moment error estimates. Unlike for the velocity error estimate, the high moment and pathwise error estimates for the pressure approximation are proved in a time-averaged norm. In addition, the impact of noise types on the rates of convergence for both velocity and pressure approximations is also addressed. Finally, numerical experiments are also provided to validate the proven theoretical results and to examine the dependence/growth of the error constants on the moment order p.
Recommended Citation
Vo, Liet. "High moment and pathwise error estimates for fully discrete mixed finite element approximations of the stochastic Stokes equations with multiplicative noise." ESAIM: Mathematical Modelling and Numerical Analysis 59, no. 3 (2025): 1301-1331.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
ESAIM: Mathematical Modelling and Numerical Analysis
DOI
10.1051/m2an/2025030
Comments
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.