In this paper, a locally stabilized finite element formulation of the Stokes problem is analyzed. A macroelement condition which is sufficient for the stability of (locally stabilized) mixed methods based on a piecewise constant pressure approximation is introduced. By satisfying this condition, the stability of the Q 1 − P 0 {Q_1} - {P_0} quadrilateral, and the P 1 − P 0 {P_1} - {P_0} triangular element, can be established.
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Kechkar et al. (1992) studied this question.
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