THE BEHAVIOR OF SEVERAL STRESS VELOCITY-PRESSURE MIXED FINITE-ELEMENTS FOR NEWTONIAN FLOWS

The Q2/P1, P2+/P1, P2/P0 and Q1/P0 velocity-pressure mixed elements ar e extended to the stress-velociy-pressure formulation, using the same interpolants for stress and velocity, and tested in the 4-to-1 contrac tion problem for Stokes flow. The comparison shows significant differe nces among them, which are not present when the velocity-pressure form ulation is used. To provide a better understanding of the phenomenon, several variants of the previous elements are introduced, obtained by either changing the pressure space or by enriching the stress space wi th bubble functions. The formulation exhibits a strong sensitivity to the first alternative, while the second produces only a minor effect. These observations are confirmed by a convergence test effected on a r egular problem with the explicit analytical solution. Also, as a resul t of the whole comparison, the P2+/P2+/P1 element looks promising for three-field calculations.