Preconditioning of a hybridizable discontinuous Galerkin method for Biot's consolidation model
By: Esteban Henríquez, Jeonghun J. Lee, Sander Rhebergen
Potential Business Impact:
Solves tricky ground problems faster.
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.
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