Incorporating variable viscosity in vorticity-based formulations for Brinkman equations
It provides a theoretical foundation for using standard Stokes finite element pairs with arbitrary vorticity spaces in Brinkman problems with variable viscosity, which is incremental for computational fluid dynamics.
The paper extends vorticity-based formulations for Brinkman equations to handle non-constant viscosity, proving optimal error estimates via Babuška-Brezzi theory and confirming them with numerical examples.
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