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) Zbl 0622.76077

Hughes, Thomas J. R.; Franca, Leopoldo P.; Balestra, Marc

Comput. Methods Appl. Mech. Eng. 59, 85-99 (1986).

[For the former parts see the above entries.]
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 \(C^ 0\) interpolations. Combinations of \(C^ 0\) 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:

76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65Z05	Applications to the sciences
76N15	Gas dynamics (general theory)
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

References:

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