  We propose a new finite element method for the three-field formulation of
Biot's consolidation model in poroelasticity and prove a priori error
estimates. Uniform-in-time error estimates of all the unknowns are obtained for
both semidiscrete solutions and fully discrete solutions with the backward
Euler time discretization. The novelty of our method is that the error analysis
does not require the assumption that the constrained specific storage
coefficient is uniformly positive. Therefore the method is guaranteed to be
locking-free without the additional assumption on material parameters.
