Speed of Convergence of Time Euler Schemes for a Stochastic 2D Boussinesq Model

We prove that an implicit time Euler scheme for the 2D Boussinesq model on the torus D converges. The various moments of the W-1,W-2 -norms of the velocity and temperature, as well as their discretizations, were computed. We obtained the optimal speed of convergence in probability, and a logarithmic speed of convergence in L-2 (Omega). These results were deduced from a time regularity of the solution both in L-2 (D) and W-1,W-2 (D), and from an L-2 (Omega) convergence restricted to a subset where the W-1,W-2 -norms of the solutions are bounded.