A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity

In this paper, we formulate a finite-element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. We approximate the flow variables by a mixed finite-element space and the displacement by a family of discontinuous Galerkin methods. Theoretical convergence error estimates are derived and, in particular, are shown to be independent of the constrained specific storage coefficient, c _o . This suggests that our proposed algorithm is a potentially effective way to combat locking, or the nonphysical pressure oscillations, which sometimes arise in numerical algorithms for poroelasticity.