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Pre-Publicación 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.

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