## Preprint 2018-22

## Veronica Anaya, Afaf Bouharguane, David Mora, Carlos Reales, Ricardo Ruiz-Baier, Nour Seloula, Hector Torres:

### Analysis and approximation of a vorticity-velocity-pressure formulation for the Oseen equations

### Abstract:

We introduce a family of mixed methods and discontinuous Galerkin discretisations designed to numerically solve the Oseen equations written in terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of the continuous problem is addressed by invoking a global inf-sup property in an adequate abstract setting for non-symmetric systems. The proposed finite element schemes, which produce exactly divergence-free discrete velocities, are shown to be well-defined and optimal convergence rates are derived in suitable norms. In addition, we establish optimal rates of convergence for a class of discontinuous Galerkin schemes, which employ stabilisation. A set of numerical examples serves to illustrate salient features of these methods.

This preprint gave rise to the following definitive publication(s):

**Veronica ANAYA, Afaf BOUHARGUANE, David MORA, Carlos REALES, Ricardo RUIZ-BAIER, Nour SELOULA, Hector TORRES: ***Analysis and approximation of a vorticity-velocity-pressure formulation for the Oseen equations*. Journal of Scientific Computing, vol. 80, 3, pp. 1577-1606, (2019).