Rotation-based mixed formulations for an elasticity-poroelasticity interface problem

Verónica Anaya, Zoa De Wijn, Bryan Gómez-Vargas, David Mora, Ricardo Ruiz-Baier

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this paper we introduce a new formulation for the stationary poroelasticity equations written using the rotation vector and the total fluid-solid pressure as additional unknowns, and we also write an extension to the elasticity-poroelasticity problem. The transmission conditions are imposed naturally in the weak formulation, and the analysis of the effective governing equations is conducted by an application of Fredholm's alternative. We also propose a monolithically coupled mixed finite element method for the numerical solution of the problem. Its convergence properties are rigorously derived and subsequently confirmed by a set of computational tests that include applications to subsurface flow in reservoirs as well as to dentistry-oriented problems.

Original languageEnglish
Pages (from-to)B225-B249
Number of pages25
JournalSIAM Journal on Scientific Computing
Volume42
Issue number1
DOIs
Publication statusPublished - 1 Jan 2020
Externally publishedYes

Keywords

  • Elasticity-poroelasticity coupling
  • Error estimation
  • Fredholm's alternative
  • Interface problems
  • Mixed finite element method

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