Stabilized finite element methods for the velocity-pressure-stress formulation of incompressible flows. (English) Zbl 0771.76033
Summary: Formulated in terms of velocity, pressure and the extra stress tensor, the incompressible Navier-Stokes equations are discretized by stabilized finite element methods. The stabilized methods proposed are analyzed for a linear model and extended to the Navier-Stokes equations. The numerical tests performed confirm the good stability characteristics of the methods. These methods are applicable to various combinations of interpolation functions, including the simplest equal-order linear and bilinear elements.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
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