Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics

We consider a two-dimensional model of double-diffusive convection and 1 its time discretisation using a second-order scheme (based on backward differentiation 2 formula for the time derivative) which treats the non-linear term explicitly. Uniform 3 bounds on the solutions of both the continuous and discrete models are derived (under 4 a timestep restriction for the discrete model), proving the existence of attractors and 5 invariant measures supported on them. As a consequence, the convergence of the 6 attractors and long time statistical properties of the discrete model to those of the 7 continuous one in the limit of vanishing timestep can be obtained following established 8 methods. 9 Mathematics Subject Classification 65M12 · 35B35 · 35K45 10