Locking-free finite element methods for poroelasticity

Ricardo Oyarzúa, Ricardo Ruiz-Baier

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29 Citations (Scopus)

Abstract

We propose a new formulation along with a family of finite element schemes for the approximation of the interaction between fluid motion and linear mechanical response of a porous medium, known as Biot's consolidation problem. The steady-state version of the system is recast in terms of displacement, pressure, and volumetric stress, and both continuous and discrete formulations are analyzed as compact perturbations of invertible problems employing a Fredholm argument. In particular, the error estimates are derived independently of the Lamé constants. Numerical results indicate the satisfactory performance and competitive accuracy of the introduced methods.

Original languageEnglish
Pages (from-to)2951-2973
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume54
Issue number5
DOIs
Publication statusPublished - 1 Jan 2016
Externally publishedYes

Keywords

  • Compact perturbation
  • Error estimates stationary flow in deformable porous media
  • Finite element approximation
  • Fredholm alternative
  • Poroelasticity
  • Volumetric stress formulation

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