On the Large Time Galerkin Approximation of the Navier–Stokes Equations

In this article we are interested in the difficult problem of relating the large time behaviour of the Navier–Stokes equations to the large time behaviour of their Galerkin approximation. We restrict ourselves to the simplest situation dealing with stationary solutions and the question is the following one; if the computed approximation of the time dependent equations “seems to converge” to some limit as t → ∞, is the same true for the exact problem and are the limits related? We give here some sufficient conditions (reasonably easy to verify) which guarantee a positive answer to this question.