Robust three-field finite element methods for Biot’s consolidation model in poroelasticity

Abstract

We propose a new finite element method for a three-field formulation of Biot’s consolidation model in poroelasticity and prove the 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. In contrast to previous results, the implicit constants in our error estimates are uniformly bounded as the Lame coefficient indicating incompressiblity of poroelastic medium is arbitrarily large, and as the constrained specific storage coefficient is arbitrarily small. Therefore the method does not suffer from the volumetric locking of linear elasticity and provides robust error estimates without additional assumptions on the constrained specific storage coefficient.