ITERATIVE STABILIZATION OF THE BILINEAR VELOCITY CONSTANT PRESSURE ELEMENT

Some finite element approximations of incompressible flows, such as those obtained with the bilinear velocity–constant pressure element (Q1−P0), are well known to be unstable in pressure while providing reasonable results for the velocity. We shall see that there exists a subspace of piecewise constant pressures that leads to a stable approximation. The main drawback associated with this subspace is the necessity of assembling groups of elements, the so‐called ‘macro‐elements’, which increases dramatically the bandwidth of the system. We study a variant of Uzawa's method which enables us to work in the desired subspace without increasing the bandwidth of the system. Numerical results show that this method is efficient and can be made to work at a low extra cost. The method can easily be generalized to other problems and is very attractive in three‐dimensional cases. Copyright © 1990 John Wiley & Sons, Ltd