The discontinuous Galerkin Interior Penalty Method with solenoidal approximations proposed in  for the incompressible Stokes equations is analyzed. Continuity and coercivity of the bilinear form are proved. A priori error estimates, with optimal convergence rates, are derived. 2D and 3D numerical examples with known analytical solution corroborate the theoretical analysis.
CitacióVillardi, A.; Fernandez, S. Analysis of the discontinuous Galerkin interior penalty method with solenoidal approximations for the stokes equations. "International journal of numerical analysis and modeling", 2014, vol. 11, núm. 4, p. 715-725.