## Preprint 2016-08

## Veronica Anaya, David Mora, Carlos Reales, Ricardo Ruiz-Baier:

### Finite element methods for a stream-function – vorticity formulation of the axisymmetric Brinkman equations

### Abstract:

This paper is devoted to the numerical analysis of a finite element approximation of the axisymmetric Brinkman equations written in terms of stream-function and vorticity fields. A mixed formulation is introduced involving appropriate weighted Sobolev spaces, and its well-posedness is analyzed using the Babuska-Brezzi theory. We introduce a suitable Galerkin discretization based on continuous piecewise polynomials of degree $k ge1$ for all the unknowns, whose solvability is established using the same framework as the continuous problem and we derive optimal a priori error estimates. A set of numerical examples are presented to illustrate the convergence and performance of the proposed schemes.

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

**Veronica ANAYA, David MORA, Carlos REALES, Ricardo RUIZ-BAIER: ***Mixed methods for a stream-function – vorticity formulation of the axisymmetric Brinkman equations*. Journal of Scientific Computing, vol. 71, 1, pp. 348-364, (2017).