  The generalized Biot-Brinkman equations describe the displacement, pressures
and fluxes in an elastic medium permeated by multiple viscous fluid networks
and can be used to study complex poromechanical interactions in geophysics,
biophysics and other engineering sciences. These equations extend on the Biot
and multiple-network poroelasticity equations on the one hand and Brinkman flow
models on the other hand, and as such embody a range of singular perturbation
problems in realistic parameter regimes. In this paper, we introduce,
theoretically analyze and numerically investigate a class of three-field finite
element formulations of the generalized Biot-Brinkman equations. By introducing
appropriate norms, we demonstrate that the proposed finite element
discretization, as well as an associated preconditioning strategy, is robust
with respect to the relevant parameter regimes. The theoretical analysis is
complemented by numerical examples.
