Continuous/Discontinuous Galerkin methods stabilized through transfer functions applied to the incompressible elasticity and to the Stokes problem

In this work, we present a family of new Continuous/Discontinuous mixed formulations with interpolation of equal order for velocity and pressure for the Stokes problem and incompressible elasticity. The degrees of freedom associated to the discontinuous component are eliminated and an approach with computational effort similar to that of the continuous formulation is obtained. An analysis of continuity and weak coercivity (InfSup condition) is performed and it is proved that the formulation is continuous and satisfies the InfSup condition on an appropriated norm. Error estimates, derived from theorems and the lemma presented are obtained on a similar norm to the one of the GLS method. Numerical experiments with the cavity problem and a smooth solution problem show the robustness of the new formulation.