  In this paper, we propose a new formulation and a suitable finite element
method for the steady coupling of viscous flow in deformable porous media using
divergence-conforming filtration fluxes. The proposed method is based on the
use of parameter-weighted spaces, which allows for a more accurate and robust
analysis of the continuous and discrete problems. Furthermore, we conduct a
solvability analysis of the proposed method and derive optimal error estimates
in appropriate norms. These error estimates are shown to be robust in the case
of large Lam\'e parameters and small permeability and storativity coefficients.
To illustrate the effectiveness of the proposed method, we provide a few
representative numerical examples, including convergence verification,
poroelastic channel flow simulation, and test the robustness of block-diagonal
preconditioners with respect to model parameters.
