  We propose a new full discretization of the Biot's equations in
poroelasticity. The construction is driven by the inf-sup theory, which we
recently developed. It builds upon the four-field formulation of the equations
obtained by introducing the total pressure and the total fluid content. We
discretize in space with Lagrange finite elements and in time with backward
Euler. We establish inf-sup stability and quasi-optimality of the proposed
discretization, with robust constants with respect to all material parameters.
We further construct an interpolant showing how the error decays for smooth
solutions.
