Suitable weak solutions of the Navier–Stokes equations constructed by a space–time numerical discretization

We prove that weak solutions obtained as limits of certain numerical space–time discretizations are suitable in the sense of Scheffer and Caffarelli–Kohn–Nirenberg. More precisely, in the space-periodic setting, we consider a full discretization in which the θ-method is used to discretize the time variable, while in the space variables we consider appropriate families of finite elements. The main result is the validity of the so-called local energy inequality.