A Hermite finite element method for incompressible fluid flow

We describe some Hermite stream function and velocity finite elements and a divergence-free finite element method for the computation of incompressible flow. Divergence-free velocity bases defined on ( but not limited to) rectangles are presented, which produce pointwise divergence-free flow fields (del.u(h) equivalent to 0). The discrete velocity satisfies a flow equation that does not involve pressure. The pressure can be recovered as a function of the velocity if needed. The method is formulated in primitive variables and applied to the stationary lid-driven cavity and backward-facing step test problems. Copyright (C) 2009 John Wiley & Sons, Ltd.