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Zbl 0622.76077
Hughes, Thomas J.R.; Franca, Leopoldo P.; Balestra, Marc
A new finite element formulation for computational fluid dynamics. V: Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. (English)
[J] Comput. Methods Appl. Mech. Eng. 59, 85-99 (1986). ISSN 0045-7825

[For the former parts see the above entries.] \par A new Petrov-Galerkin formulation of the Stokes problem is proposed. The new formulation possesses better stability properties than the classical Galerkin/variational method. An error analysis is performed for the case in which both the velocity and pressure are approximated by $C\sp 0$ interpolations. Combinations of $C\sp 0$ interpolations which are unstable according to the Babuška-Brezzi condition (e.g., equal-order interpolations) are shown to be stable and convergent within the present framework. Calculations exhibiting the good behavior of the methodology are presented.

MSC 2000:: *76N10 Compressible fluids, general
65Z05 Applications to physics
76N15 Gas dynamics, general
76R99 Diffusion and convection

Keywords: Petrov-Galerkin formulation; Stokes problem; Galerkin/variational method; error analysis; interpolations; Babuška-Brezzi condition; equal-order interpolations

Citations: Zbl 0587.76120; Zbl 0581.76077; Zbl 0572.76068; Zbl 0622.76075; Zbl 0622.76074; Zbl 0622.76076

Cited in: Zbl 0766.76050 Zbl 0760.76051 Zbl 0696.76034 Zbl 0686.76016 Zbl 0669.76052 Zbl 0635.76067 Zbl 0635.76066 Zbl 0622.76075 Zbl 0622.76074 Zbl 0587.76120

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