A finite element for the numerical solution of viscous incompressible flows

A finite element of the penalization type for the solution of incompressible viscous Navier-Stokes equations using an isoparametric parabolic element is presented. The penalization of the continuity equation is implemented by means of a reduced integration technique, thus eliminating the pressure unknown from the system of equations to be solved. The superiority of the nine-node isoparametric quadrilateral element over the eight-node element is discussed. Stability and convergence properties of the method are illustrated by means of various numerical examples.