New stabilized mixed finite element methods for two-field poroelasticity with low permeability

Abstract

In this paper, we develop new stabilized mixed finite element (MFE) methods for two-field Biot's model of poroelasticity. We employ the H(div)-conforming element and discontinuous element to approximate the displacement and pressure variables, and use the θ-scheme to discretize time. By adding the stabilization term based on polynomial pressure projection, the fully-discrete and stabilized MFE methods are obtained. Our methods work well for both inf-sup stable and unstable element pairs, and provide oscillation-free pressure solutions in heterogeneous materials with low-permeable layers or interfaces. These methods are also volumetric locking-free and locally mass-conservative. We establish optimal a priori error estimates and perform numerical examples, which show the uniform robustness of the proposed methods for low permeability.