  In this paper we propose a new finite element discretization for the
two-field formulation of poroelasticity which uses the elastic displacement and
the pore pressure as primary variables. The main goal is to develop a numerical
method with small problem sizes which still achieve key features such as
parameter-robustness, local mass conservation, and robust preconditionor
construction. For this we combine a nonconforming finite element and the
interior over-stabilized enriched Galerkin methods with a suitable
stabilization term. Robust a priori error estimates and parameter-robust
preconditioner construction are proved, and numerical results illustrate our
theoretical findings.
