A comparison of two nonconforming finite element methods for linear three-field poroelasticity

Abstract

We present and analyze two kinds of nonconforming finite element methods for three-field Biot’s consolidation model in poroelasticity. We employ the Crouzeix-Raviart element for one of the displacement component and conforming linear element for the remaining component, the lowest order Raviart-Thomas element (or the first-order Brezzi-Douglas-Marini element) for the fluid flux, and the piecewise constant for the pressure. We provide the corresponding analysis, including the well-posedness and a priori error estimates, for the fully discrete scheme coupled with the backward Euler finite difference for the time discretization. Such scheme ensures that the discrete Korn’s inequality is satisfied without adding any stabilization terms. In particular, it is free of poroelasticity locking. Numerical results are presented to compare the accuracy and locking-free performance of the two introduced schemes.

Keywords

• biot’s consolidation model
• nonconforming finite element method
• poroelasticity locking
• locking-free
• 65n30
• 74s05