Stabilized Finite Element Methods for the Velocity-Pressure-Stress Formulation of Incompressible Flows

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.