Analysis of locally stabilized mixed finite element methods for the Stokes problem

Kechkar, Nasserdine; Silvester, David

doi:10.1090/S0025-5718-1992-1106973-X

Analysis of locally stabilized mixed finite element methods for the Stokes problem
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by Nasserdine Kechkar and David Silvester PDF

Math. Comp. 58 (1992), 1-10 Request permission

Abstract:

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.

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