Locking-Free and Locally-Conservative Enriched Galerkin Method for Poroelasticity

This paper develops a new coupled enriched Galerkin (EG) scheme for Biot's poroelasticity model based on the displacement-pressure formulation. The aim of this work is to provide a stable and robust numerical method for a wide range of physical and numerical parameters. The finite-dimensional solution spaces are enriched linear Lagrange spaces, and the inf-sup condition between the two spaces is achieved by adding a stabilization term. The resulting coupled EG method is locally conservative and provides stable solutions without spurious oscillations or overshoots/undershoots. The well-posedness and optimal a priori error estimates are established. Numerical results in various scenarios are provided.