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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.

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
Full Text: DOI
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