Analysis of an embedded-hybridizable discontinuous Galerkin method for Biot's consolidation model

TL;DR

This paper introduces a stable embedded-hybridizable discontinuous Galerkin method for Biot's poroelasticity model, providing error estimates and demonstrating its locking-free property through numerical validation.

Contribution

It develops a novel embedded-hybridizable DG approach for Biot's model, ensuring stability and locking-free discretization with proven error bounds.

Findings

The method is stable and well-posed.

Numerical examples confirm locking-free behavior.

Error estimates demonstrate accuracy of the discretization.

Abstract

We present an embedded-hybridizable discontinuous Galerkin finite element method for the total pressure formulation of the quasi-static poroelasticity model. Although the displacement and the Darcy velocity are approximated by discontinuous piece-wise polynomials, $H(\text{div})$-conformity of these unknowns is enforced by Lagrange multipliers. The semi-discrete problem is shown to be stable and the fully discrete problem is shown to be well-posed. Additionally, space-time a priori error estimates are derived, and confirmed by numerical examples, that show that the proposed discretization is free of volumetric locking.