The CIP method embedded in finite element discretizations of incompressible fluid flows

Quite effective low-order finite element and finite volume methods for incompressible fluid flows have been established and are widely used. However, higher-order finite element methods that are stable, have high accuracy and are computationally efficient are still sought. Such discretization schemes could be particularly useful to establish error estimates in numerical solutions of fluid flows. The objective of this paper is to report on a study in which the cubic interpolated polynomial (CIP) method is embedded into 4-node and 9-node finite element discretizations of 2D flows in order to stabilize the convective terms. To illustrate the capabilities of the formulations, the results obtained in the solution of the driven flow square cavity problem are given. Copyright q 2006 John Wiley & Sons, Ltd