## Preprint 2019-17

## Veronica Anaya, Bryan Gomez-Vargas, David Mora, Ricardo Ruiz-Baier:

### Incorporating variable viscosity in vorticity-based formulations for Brinkman equations

### Abstract:

In this brief note, we introduce a non-symmetric mixed finite element formulation for Brinkman equations written in terms of velocity, vorticity and pressure with non-constant viscosity. The analysis is performed by the classical Babuška-Brezzi theory, and we state that any inf-sup stable finite element pair for Stokes approximating velocity and pressure can be coupled with a generic discrete space of arbitrary order for the vorticity. We establish optimal a priori error estimates which are further confirmed through computational examples.

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

**Veronica ANAYA, Bryan GOMEZ-VARGAS, David MORA, Ricardo RUIZ-BAIER: ***Incorporating variable viscosity in vorticity-based formulations for Brinkman equations*. Comptes Rendus Mathematique, vol. 357, 6, pp. 552-560, (2019).