Discontinuous spectral element approximations for the velocity-pressure-stress formulation of the Stokes problem

The discretization of the mixed velocity{pressure{stress formulation of the Stokes problem using the spectral element method is considered. The compatibility conditions between the discrete velocity and extra stress spaces are examined. A su cient condition for compatibility, namely that the discrete extra stress space con- tains the gradient of the discrete velocity space, is satis ed provided one allows discontinuous approximations of the extra stress between elements. Numerical results are presented for smooth and non-smooth problems showing the consequences of satisfying or violating this condition