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Analysis of locally stabilized mixed finite element methods for the Stokes problem. (English) Zbl 0738.76040
Summary: 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 \(Q_ 1-P_ 0\) quadrilateral, and the \(P_ 1-P_ 0\) triangular element, can be established.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
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