  We study the a priori error analysis of finite element methods for Biot's
consolidation model. We consider a formulation which has the stress tensor, the
fluid flux, the solid displacement, and the pore pressure as unknowns. Two
mixed finite elements, one for linear elasticity and the other for mixed
Poisson problems are coupled for spatial discretization, and we show that any
pair of stable mixed finite elements is available. The novelty of our analysis
is that the error estimates of all the unknowns are robust for material
parameters. Specifically, the analysis does not need a uniformly positive
storage coefficient, and the error estimates are robust for nearly
incompressible materials. Numerical experiments illustrating our theoretical
analysis are included.
