Strong L^2 convergence of time Euler schemes for stochastic 3D Brinkman–Forchheimer–Navier–Stokes equations

Hakima Bessaih (1) , Annie Millet (2, 3)

1 FIU - Florida International University [Miami]
2 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
3 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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 {\color{blue} 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, {\color{blue} that is} independent of the viscosity parameter.

Mots clés: Stochastic Navier-Sokes equations; time Euler schemes; strong convergence; implicit time discretization; Brinkman Forchheimer

Domaines: Probabilités [math.PR]

Hakima Bessaih, Annie Millet. Strong L^2 convergence of time Euler schemes for stochastic 3D Brinkman–Forchheimer–Navier–Stokes equations. Stochastics and Partial Differential Equations: Analysis and Computations, 2022, 10 (3), pp.1005-1049. ⟨10.1007/s40072-022-00255-9⟩. ⟨hal-03793912⟩