An efficient discretization for a family of Time Relaxation models

In this paper, we present a finite element study for the family of Time Relaxation models using the recently proposed EMAC discretization of the non-linear term. This discretization conserves energy, momentum and angular momentum. We study the conservation properties, stability and error estimates in the fully discrete case. Comparisons with the classical skew symmetric non-linear formulation are drawn throughout the paper. We will show that the error estimate for EMAC is improved over the skew symmetric scheme based on the constant obtained from the application of Gronwall’s inequality. Numerical experiments in 2D and 3D showing the advantage of EMAC over skew symmetric are performed as well. •Finite element stability and error estimates in the fully discrete case for regularized Navier–Stokes equations.•Comparisons of EMAC non-linear formulation with the classical skew symmetric are drawn.•Numerical experiments showing the advantage of studied work.