APPROXIMATION OF THE STATIONARY STATISTICAL PROPERTIES OF THE DYNAMICAL SYSTEM GENERATED BY THE TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION PROBLEM

In this article, we consider a temporal linear semi-implicit approximation of the two-dimensional Rayleigh–Benard convection problem. We prove that the stationary statistical properties as well as the global attractors of this linear semi-implicit scheme converge to those of the 2D Rayleigh–Benard problem as the time step approaches zero.

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