Green's Function Representation and Numerical Approximation of the Two-dimensional Stochastic Stokes Equation
Abstract
This paper investigates the two-dimensional unsteady Stokes equation with general additive noise. The primary contribution is the derivation of the relevant estimate of Green's tensor, which provides a fundamental representation for the solution of this stochastic equation. We demonstrate the crucial role of Green's function in understanding the stability and perturbation characteristics of the stochastic Stokes system. Furthermore, we analyze the convergence properties of the Euler–Maruyama (EM) scheme for temporal discretization and derive error estimates for a Galerkin finite element discretization using the Taylor–Hood method for spatial approximation. This work provides a strong convergence of order [Formula presented] of the velocity in the L2(0,T;L2(D)) norm and [Formula presented] of the pressure in the L2(0,T;H−1(D)) norm based on the Green tensor approach. These results contribute to a deeper understanding of the stochastic behavior of fluid dynamics systems, paving the way for improved theoretical modeling and more accurate numerical simulations in diverse fields such as meteorology, oceanography, and engineering applications.
Recommended Citation
J. Zhu et al., "Green's Function Representation and Numerical Approximation of the Two-dimensional Stochastic Stokes Equation," Engineering Analysis with Boundary Elements, vol. 172, article no. 106117, Elsevier, Mar 2025.
The definitive version is available at https://doi.org/10.1016/j.enganabound.2025.106117
Department(s)
Mathematics and Statistics
Keywords and Phrases
Error estimates; Euler–Maruyama scheme; Finite element method; Green tensor; Q-Wiener process; Stochastic Stokes equation
International Standard Serial Number (ISSN)
0955-7997
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 Elsevier, All rights reserved.
Publication Date
01 Mar 2025
