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Stabilized finite element formulations for incompressible flow computations. (English) Zbl 0747.76069

This work consists of a review of the stabilized finite element formulations designed to prevent the potential numerical instabilities just described. The stabilization techniques that are reviewed more extensively than others are the Galerkin/least-squares (GLS), streamline- upwind/Petrov-Galerkin (SUPG), and pressure-stabilizing/Petrov-Galerkin (PSPG) formulations. All these formulations are consistent in the sense that, for reasons to be explained soon, an exact solution still satisfies the stabilized formulation. After introduction, in Section II, the governing equations of the unsteady incompressible flows are reviewed. The review of the space-time and GLS formulations is presented in Section III. The SUPG and PSPG stabilizations are reviewed in Section IV. In Section V, as an application to moving boundaries and interfaces, the DSD/ST procedure is reviewed. Sections III, IV, and V include numerical examples for the methods reviewed in those sections. Concluding remarks are given in Section VI.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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