New stabilized discretizations for poroelasticity equations

Francisco J. Gaspar, Carmen Rodrigo, Xiaozhe Hu, Peter Ohm, James Adler, Ludmil Zikatanov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationNumerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers
EditorsNatalia Kolkovska, Krassimir Georgiev, Geno Nikolov
PublisherSpringer Verlag
Pages3-14
Number of pages12
ISBN (Print)9783030106911
DOIs
StatePublished - 2019
Event9th International conference on Numerical Methods and Applications, NMA 2018 - Borovets, Bulgaria
Duration: Aug 20 2018Aug 24 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11189 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference9th International conference on Numerical Methods and Applications, NMA 2018
CountryBulgaria
CityBorovets
Period8/20/188/24/18

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Gaspar, F. J., Rodrigo, C., Hu, X., Ohm, P., Adler, J., & Zikatanov, L. (2019). New stabilized discretizations for poroelasticity equations. In N. Kolkovska, K. Georgiev, & G. Nikolov (Eds.), Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers (pp. 3-14). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11189 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-10692-8_1