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

We prove that some time Euler schemes for the 3D Navier-Stokes equations modified by adding a Brinkman-Forchheimer term and subject to a random perturbation converge in mean square. This extends previous results about the strong speed of convergence of some time discretization schemes for the 2D Navier Stokes equations. Unlike in the 2D case, in our 3D model the Brinkman-Forchheimer term enables to obtain a strong speed of convergence of order almost 1/2 independent of the viscosity parameter.