New subgrid artificial viscosity Galerkin methods for the Navier–Stokes equations

We study subgrid artificial viscosity methods for approximating solutions to the Navier–Stokes equations. Two methods are introduced that add viscous stabilization via an artificial viscosity, then remove it only on a coarse mesh. These methods can be considered as conforming, mixed methods, the first for velocity and vorticity, and the second for velocity and its gradient, the former incorporating a naturally arising grad–div stabilization term. In this paper, we rigorously study the first scheme analytically, showing that it is unconditionally stable and optimally convergent, as well as both schemes computationally. Numerical experiments demonstrate the advantages of both of these methods.