Bubble stabilization of discontinuous Galerkin methods

We analyze the stabilizing effect of the introduction of suitable bubble functions in DG formulations for linear second order elliptic problems, working, for the sake of simplicity, on Laplace operator. In particular we analyze the non-symmetric formulation of Baumann–Oden on rather general decompositions, and we show that the piecewise linear discontinuous approximation, without jump stabilization, can be used if suitable bubbles are added to the local spaces.