Consistent vs. reduced integration penalty methods for incompressible media using several old and new elements

The frequently used reduced integration method for solving incompressible flow problems ‘a la penalty’ is critically examined vis‐a‐vis the consistent penalty method. For the limited number of quadrilateral and hexahedral elements studied, it is shown that the former method is only equivalent to the latter in certain special cases. In the general case, the consistent penalty method is shown to be more accurate. Finally, we demonstrate significant advantages of a new element, employing biquadratic (2‐D) or triquadratic (3‐D) velocity and linear pressure over that using the same velocity but employing bilinear (2‐D) or trilinear (3‐D) pressure approximation.