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Mathematics of Computation

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

Authors: Nasserdine Kechkar and David Silvester
Journal: Math. Comp. 58 (1992), 1-10
MSC: Primary 65N15; Secondary 65N30, 76D07, 76M10
MathSciNet review: 1106973
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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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Keywords: Stabilized finite element, Stokes equation
Article copyright: © Copyright 1992 American Mathematical Society