Strong $l$ convergence of time numerical schemes for the stochastic two-dimensional Navier-Stokes equations
Article
Bessaih, H, Millet, A. (2019). Strong $l$ convergence of time numerical schemes for the stochastic two-dimensional Navier-Stokes equations
. 39(4), 2135-2167. 10.1093/imanum/dry058
Bessaih, H, Millet, A. (2019). Strong $l$ convergence of time numerical schemes for the stochastic two-dimensional Navier-Stokes equations
. 39(4), 2135-2167. 10.1093/imanum/dry058
We prove that some time discretization schemes for the two-dimensional Navier-Stokes equations on the torus subject to a random perturbation converge in $L^2(\varOmega) $. This refines previous results that established the convergence only in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic Navier-Stokes equations and convergence of a localized scheme we can prove strong convergence of fully implicit and semiimplicit temporal Euler discretizations and of a splitting scheme. The speed of the $L^2(\varOmega) $ convergence depends on the diffusion coefficient and on the viscosity parameter.
