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arXiv · 2508.12991

Preconditioning of a hybridizable discontinuous Galerkin method for Biot's consolidation model

Esteban Henríquez·Jeonghun J. Lee·Sander Rhebergen
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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.

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Esteban Henríquez, Jeonghun J. Lee, Sander Rhebergen. 2025-08-18. Preconditioning of a hybridizable discontinuous Galerkin method for Biot's consolidation model. https://arxiv.org/abs/2508.12991

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