Work

High moment and pathwise error estimates for fully discrete mixed finite element approximations of the stochastic Stokes equations with multiplicative noise

Year: 2025

Type: article

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 two fully discrete mixed finite element discretizations. Optimal rates of convergence are established for all p th moment errors for p ≥2 using a novel bootstrap 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 .

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2025030

Author: Liet Vo

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funder: National Science Foundation

Award: Novel numerical methods for fully nonlinear second order elliptic and parabolic Monge-Ampere and Hamilton-Jacobi-Bellman equations