Numerical analysis of 2D Navier--Stokes equations with additive stochastic forcing
Numerical Analysis
2022-03-23 v2 Numerical Analysis
Analysis of PDEs
Probability
Abstract
We propose and study a temporal, and spatio-temporal discretisation of the 2D stochastic Navier--Stokes equations in bounded domains supplemented with no-slip boundary conditions. Considering additive noise, we base its construction on the related nonlinear random PDE, which is solved by a transform of the solution of the stochastic Navier--Stokes equations. We show strong rate (up to) in probability for a corresponding discretisation in space and time (and space-time). Convergence of order (up to) 1 in time was previously only known for linear SPDEs.
Keywords
Cite
@article{arxiv.2110.05894,
title = {Numerical analysis of 2D Navier--Stokes equations with additive stochastic forcing},
author = {Dominic Breit and Andreas Prohl},
journal= {arXiv preprint arXiv:2110.05894},
year = {2022}
}