| Abstract: |
| We prove the strong (i.e. in the set of square integrable random variables) convergence of a fully or semi-implicit time discretization,
as well as of a full space-time discretization based on finite elements, of the 2D Navier-Stokes equations on the torus subject to a random perturbation.
The initial condition belongs to in $H^1$ ; it is deterministic or has exponential moments.
The speed of convergence is polynomial in case of an additive noise; it depends on the viscosity and the strength of the noise.
The argument is based on convergence of a localized scheme, and on exponential moments of the solution to the stochastic 2D Navier-Stokes
equations, and of its fully implicit time scheme.
This work improves previous results which only described the speed of convergence in probability
of these numerical schemes. |
|