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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

[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 Compressible fluids, general 65Z05 Applications of numerical analysis to physics 76N15 Gas dynamics, general 76R99 Diffusion and convection (fluid mechanics)