Strong L2 convergence of time Euler schemes for stochastic 3D Brinkman-Forchheimer-Navier-Stokes equations

TL;DR

This paper proves strong L2 convergence of Euler schemes for a 3D stochastic Brinkman-Forchheimer-Navier-Stokes model, achieving near 1/2 order convergence independent of viscosity.

Contribution

It extends convergence results from 2D to 3D Navier-Stokes equations with Brinkman-Forchheimer term under stochastic perturbations.

Findings

Convergence in L2(Ω) for the 3D model.

Near 1/2 order strong convergence rate.

Independence from viscosity parameter.

Abstract

We prove that some time Euler schemes for the 3D Navier-Stokes equations modified by adding a Brinkman-Forchheimer term and a random perturbation converge in $L^2(\Omega)$. This extends previous results concerning the strong rate of convergence of some time discretization schemes for the 2D Navier Stokes equations. Unlike the 2D case, our proposed 3D model with the Brinkman-Forchheimer term allows for a strong rate of convergence of order almost 1/2, that is independent of the viscosity parameter.