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 arXiv:2503.05918, 2025 to show that a reduced form of the preconditioner is also parameter-robust for the reduced HDG discretization. We verify the parameter-robustness of the preconditioner through numerical examples in both two and three dimensions.
Henríquez et al. (Mon,) studied this question.