  A stable finite element scheme that avoids pressure oscillations for a
three-field Biot's model in poroelasticity is considered. The involved
variables are the displacements, fluid flux (Darcy velocity), and the pore
pressure, and they are discretized by using the lowest possible approximation
order: Crouzeix-Raviart finite elements for the displacements, lowest order
Raviart-Thomas-Nedelec elements for the Darcy velocity, and piecewise constant
approximation for the pressure. Mass lumping technique is introduced for the
Raviart-Thomas-Nedelec elements in order to eliminate the Darcy velocity and,
therefore, reduce the computational cost. We show convergence of the discrete
scheme which is implicit in time and use these types of elements in space with
and without mass lumping. Finally, numerical experiments illustrate the
convergence of the method and show its effectiveness to avoid spurious pressure
oscillations when mass lumping for the Raviart-Thomas-Nedelec elements is used.
