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2004-02

Pressure Separation - a Technique for Improving the Velocity Error in Finite Element Discretisations of the Navier-Stokes Equations

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