Abstract:We prove the convergence of certain second-order numerical methods to weak solutions of the Navier-Stokes equations satisfying in addition the local energy inequality, and therefore suitable in the sense of Scheffer and Caffarelli-Kohn-Nirenberg. More precisely, we treat the space-periodic case in three space-dimensions and we consider a full discretization in which the the classical Crank-Nicolson method (θ-method with θ = 1/2) is used to discretize the time variable, while in the space variables we consider … Show more
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