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