A stable enriched Galerkin element for the Stokes problem

We propose a stable element for the divergence operator that approximates the velocity by continuous linear polynomials plus piecewise constants and the pressure by piecewise constants. A uniform inf-sup condition is obtained for conforming meshes in two or three dimensions. The resulting method belongs to the class of enriched Galerkin methods, and is applied to the solution of a Stokes system. A priori error estimates in the energy norm and in the L2 norm are derived. Extensions to the Navier-Stokes system are presented.