  In this paper we consider a three-field formulation of the Biot model which
has the displacement, the total pressure, and the pore pressure as unknowns.
For parameter-robust stability analysis, we first show a priori estimates of
the continuous problem with parameter-dependent norms. Then we study finite
element discretizations which provide parameter-robust error estimates and
preconditioners. For finite element discretizations we consider standard mixed
finite element as well as stabilized methods for the Stokes equations, and the
complete error analysis of semidiscrete solutions is given. Abstract forms of
parameter-robust preconditioners are investigated by the operator
preconditioning approach. The theoretical results are illustrated with
numerical experiments.
