  This paper concentrates on a priori error estimates of two fully discrete
coupled schemes for Biot's consolidation model based on the three-field
formulation introduced by Oyarzua et al. (SIAM Journal on Numerical Analysis,
2016). The spatial discretizations are based on the Taylor-Hood finite elements
combined with Lagrange elements for the three primary variables. For time
discretization, we consider two methods. One uses the backward Euler method,
and the other applies a combination of the backward Euler and Crank-Nicolson
methods. A priori error estimates show that the two schemes are unconditionally
convergent with optimal error orders. Detailed numerical experiments are
presented to validate the theoretical analysis.
