by Sashikumaar Ganesan, Volker John.

**Series:** 2004-02, Preprints

- MSC:
- 65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

**Abstract:**

This paper presents a technique to improve the velocity error in

finite element solutions of the steady state Navier-Stokes

equations. This technique is called pressure separation. It relies

upon subtracting the gradient of an appropriate approximation of the

pressure on both sides of the Navier-Stokes equations. With this, the

finite element error estimate can be improved in the case of higher

Reynolds numbers. For practical reasons, the pressure separation can

be applied above all for finite

element discretisations of the Navier-Stokes equations with piecewise

constant pressure. This paper

presents a computational study of five ways to compute an appropriate

approximation of the pressure. These ways are assessed on two- and

three-dimensional examples. They are compared with respect to the

error reduction in the discrete velocity and the computational

overhead.

**Keywords:**

steady state Navier-Stokes equatio