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Stabilised bilinear-constant velocity-pressure finite elements for the conjugate gradient solution of the Stokes problem. (English) Zbl 0706.76075
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 ${Q}_{1}-{P}_{0}$ 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:
 76M10 Finite element methods (fluid mechanics) 76D07 Stokes and related (Oseen, etc.) flows