Robust Approximation of Generalized Biot-Brinkman Problems

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