Using the standard mixed Galerkin methods with equal order elements to
solve Biot’s consolidation problems, the pressure close to the initial time produces
large non-physical oscillations. In this paper, we propose a class of fully discrete stabilized
methods using equal order elements to reduce the effects of non-physical oscillations.
Optimal error estimates for the approximation of displacements and pressure at
every time level are obtained, which are valid even close to the initial time. Numerical
experiments illustrate and confirm our theoretical analysis.