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Zbl 0706.76075
Silvester, D.J.; Kechkar, N.
Stabilised bilinear-constant velocity-pressure finite elements for the conjugate gradient solution of the Stokes problem. (English)
[J] Comput. Methods Appl. Mech. Eng. 79, No.1, 71-86 (1990). ISSN 0045-7825

Summary: In this paper, a sufficient condition for the stability of low-order mixed finite element methods is introduced. To illustrate the possibilities, two stabilization procedures for the popular $Q\sb 1-P\sb 0$ mixed method are theoretically analyzed. The effectiveness of these procedures in practice is assessed by comparing results with those obtained using a conventional penalty formulation, for a standard test problem. It is demonstrated that with appropriate stabilization, efficient iterative solution techniques of conjugate gradient type can be applied directly to the discrete Stokes system.

MSC 2000:: *76M10 Finite element methods
76D07 Stokes flows

Keywords: sufficient condition; stability of low-order mixed finite element methods; stabilization procedures; penalty formulation; discrete Stokes system

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Zentralblatt MATH Berlin [Germany]