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New Stabilized Discretizations for Poroelasticity Equations

  • Francisco J. GasparEmail author
  • Carmen Rodrigo
  • Xiaozhe Hu
  • Peter Ohm
  • James Adler
  • Ludmil Zikatanov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11189)

Abstract

In this work, we consider two discretizations of the three-field formulation of Biot’s consolidation problem. They employ the lowest-order mixed finite elements for the flow (Raviart-Thomas-Nédélec elements for the Darcy velocity and piecewise constants for the pressure) and are stable with respect to the physical parameters. The difference is in the mechanics: one of the discretizations uses Crouzeix-Raviart nonconforming linear elements; the other is based on piecewise linear elements stabilized by using face bubbles, which are subsequently eliminated. The numerical solutions obtained from these discretizations satisfy mass conservation: the former directly and the latter after a simple postprocessing.

Keywords

Stable finite elements Poroelasticity equations Mass conservation 

Notes

Acknowledgements

The work of F. J. Gaspar is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement NO 705402, POROSOS. The research of C. Rodrigo is supported in part by the Spanish project FEDER /MCYT MTM2016-75139-R and the DGA (Grupo consolidado PDIE). The work of Zikatanov was partially supported by NSF grants DMS-1720114 and DMS-1819157. The work of Adler, Hu, and Ohm was partially supported by NSF grant DMS-1620063.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Centrum Wiskunde & Informatica (CWI)AmsterdamThe Netherlands
  2. 2.IUMA and Department of Applied MathematicsUniversity of ZaragozaZaragozaSpain
  3. 3.Department of MathematicsTufts UniversityMedfordUSA
  4. 4.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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