A poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

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Abstract
The calculation of pressures when the penalty function approximation is used in finite element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.