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) |