Preprint A350/2004
Continuous Q1-Q1 Stokes elements stabilized with non-conforming null edge average velocity functions

Marcus Sarkis | Franca , Leopoldo | Oliveira, Saulo

**Keywords: **
Stokes | Finite Element | inf-sup | stabilization | bubble function

We present a stabilized finite element method for Stokes equations
with piecewise continuous bilinear approximations for both
velocity and pressure variables. The velocity field is enriched
with piecewise polynomial bubble functions with null average at element edges.
These functions are statically condensed at the element level
and therefore they can be viewed as a continuous Q1-Q1 stabilized
finite element method. The enriched velocity-pressure pair satisfies
optimal inf-sup conditions and approximation properties.
Numerical experiments show that the proposed
discretization outperforms the Galerkin least-squares method.