Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form

Ruben Caraballo, Chansophea Wathanak In, Alberto F. Martín, Ricardo Ruiz-Baier

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this article, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of parameter-weighted spaces, which allows for a more accurate and robust analysis of the continuous and discrete problems. Furthermore, we conduct a solvability analysis of the proposed method and derive optimal error estimates in appropriate norms. These error estimates are shown to be robust in a variety of regimes, including the case of large Lamé parameters and small permeability and storativity coefficients. To illustrate the effectiveness of the proposed method, we provide a few representative numerical examples, including convergence verification and testing of robustness of block-diagonal preconditioners with respect to model parameters.

Original languageEnglish
Article numbere23083
Number of pages26
JournalNumerical Methods for Partial Differential Equations
Volume40
Issue number3
DOIs
Publication statusPublished - May 2024

Keywords

  • Biot–Brinkman coupled problem
  • deformable porous media
  • mixed finite element methods
  • vorticity-based formulation

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