Bubble-stabilized spectral methods for the incompressible Navier-Stokes equations Original Research Article

We present and investigate a stabilized spectral Legendre schemefor approximating the incompressible Navier-Stokes equations. The stabilization is obtained by addinglocal bubble functions to the usual global polynomial trial and testvelocities. This modification allows the use of equal degree velocities andpressures; furthermore, in the advection-dominated regime, it induces an effectsimilar to the SUPG-effect in finite elements. The method is validated on a Stokes flow and onthe regularized driven cavity flow at different Reynolds regimes; acomparison with other spectral and finite element schemes is also provided.