Preconditioning of a Hybridizable Discontinuous Galerkin Method for Biot’s Consolidation Model

Abstract

We present a parameter-robust preconditioner for a hybridizable discontinuous Galerkin (HDG) discretization of a four-field formulation of Biot’s consolidation model. We first determine a parameter-robust preconditioner for the full discretization. HDG methods, however, allow for static condensation. We therefore apply the framework presented in our previous work (SIAM J Sci Comput 47:A3212–A3238, 2025) to show that a reduced form of the preconditioner is also parameter-robust for the reduced HDG discretization. The proposed preconditioner is robust with respect to parameters of the model, which may vary over several orders of magnitude, and the mesh size. We verify this parameter-robustness of the preconditioner through numerical examples in both two and three dimensions.