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

Abstract

We prove that an implicit time Euler scheme for the 2D Boussinesq model on the torus D converges. The various moments of the W1,2-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 L2(Ω). These results were deduced from a time regularity of the solution both in L2(D) and W1,2(D), and from an L2(Ω) convergence restricted to a subset where the W1,2-norms of the solutions are bounded.