# Robust Block Preconditioners for Biot's Model

## TL;DR

This paper develops and analyzes robust block preconditioners for Biot's consolidation model, ensuring efficiency and stability across various parameters using stabilized finite-element discretizations.

## Contribution

It introduces new block preconditioners based on well-posedness, proven to be robust against physical and discretization parameters.

## Key findings

- Preconditioners are robust with respect to model parameters.
- Numerical results confirm theoretical robustness.
- Block diagonal and triangular preconditioners are effective.

## Abstract

In this paper, we design robust and efficient block preconditioners for the two-field formulation of Biot's consolidation model, where stabilized finite-element discretizations are used. The proposed block preconditioners are based on the well-posedness of the discrete linear systems. Block diagonal (norm-equivalent) and block triangular preconditioners are developed, and we prove that these methods are robust with respect to both physical and discretization parameters. Numerical results are presented to support the theoretical results.