Preconditioning of a hybridizable discontinuous Galerkin method for Biot's consolidation model
Numerical Analysis
2025-08-19 v1 Numerical Analysis
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 [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.
Keywords
Cite
@article{arxiv.2508.12991,
title = {Preconditioning of a hybridizable discontinuous Galerkin method for Biot's consolidation model},
author = {Esteban Henríquez and Jeonghun J. Lee and Sander Rhebergen},
journal= {arXiv preprint arXiv:2508.12991},
year = {2025}
}