Veronica Anaya, David Mora, Carlos Reales, Ricardo Ruiz-Baier:
Finite element methods for a stream-function – vorticity formulation of the axisymmetric Brinkman equations
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).