Bubble stabilized discontinuous Galerkin method for stokes' problem

We propose a low order discontinuous Galerkin method for incompressible flows. Stability of the discretization of the Laplace operator is obtained by enriching the space elementwise with a non-conforming quadratic bubble. Several possible pressure spaces that lead to uniformly stable velocity pressure pairs are proposed. We prove optimal convergence estimates and local conservation of both mass and linear momentum independent of numerical parameters.