Mixed interpolation in primitive variable finite element formulations for incompressible flow

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Abstract
This paper shows that mixed interpolation is required because of the nature of the pressure terms in the equations. These lead to finite element equations which in many circumstances do not uniquely determine the pressure, if the same interpolations are used for pressure and velocities.Several new combinations of pressure and velocity interpolation are analysed with the aid of a novel diagrammatic technique. In particular we consider some very interesting combinations in which, over nearly all the flow, the pressure and velocity are approximated on elements by biquadratic polynomials which are continuous across element boundaries.The theory of this paper is shown to be in complete agreement with numerical experiment.

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