Numerical analysis of two-dimensional Navier–Stokes equations with additive stochastic forcing

Author:

Breit Dominic1,Prohl Andreas2

Affiliation:

1. Department of Mathematics, Heriot-Watt University , Riccarton, Edinburgh EH14 4AS, UK

2. Mathematical Institute, University of Tübingen , Auf der Morgenstelle 10, 72076 Tübingen, Germany

Abstract

Abstract We propose and study a temporal and a spatio-temporal discretisation of the two-dimensional 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 partial differential equation, which is solved by a transform of the solution of the stochastic Navier–Stokes equations. We show a strong rate (up to) $1$ in probability for a corresponding discretisation in space and time (and space-time).

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Numerical method and error estimate for stochastic Landau–Lifshitz–Bloch equation;IMA Journal of Numerical Analysis;2024-08-10

2. Weak error analysis for the stochastic Allen–Cahn equation;Stochastics and Partial Differential Equations: Analysis and Computations;2024-02-22

3. Space-Time Approximation of Local Strong Solutions to the 3D Stochastic Navier–Stokes Equations;Computational Methods in Applied Mathematics;2023-08-08

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