Guaranteed locking-free finite element methods for Biot's consolidation model in poroelasticity

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.