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 - Jan 1 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

Fingerprint

Poroelasticity
Consolidation
Conservation
Mechanics
Discretization
Mass Conservation
Mixed Finite Elements
Post-processing
Piecewise Linear
Bubble
Lowest
Numerical Solution
Face
Formulation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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
Gaspar, Francisco J. ; Rodrigo, Carmen ; Hu, Xiaozhe ; Ohm, Peter ; Adler, James ; Zikatanov, Ludmil. / New stabilized discretizations for poroelasticity equations. Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers. editor / Natalia Kolkovska ; Krassimir Georgiev ; Geno Nikolov. Springer Verlag, 2019. pp. 3-14 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{6c8a1a20cc05482c96959247d15168eb,
title = "New stabilized discretizations for poroelasticity equations",
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-N{\'e}d{\'e}lec 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.",
author = "Gaspar, {Francisco J.} and Carmen Rodrigo and Xiaozhe Hu and Peter Ohm and James Adler and Ludmil Zikatanov",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/978-3-030-10692-8_1",
language = "English (US)",
isbn = "9783030106911",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "3--14",
editor = "Natalia Kolkovska and Krassimir Georgiev and Geno Nikolov",
booktitle = "Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers",
address = "Germany",

}

Gaspar, FJ, 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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11189 LNCS, Springer Verlag, pp. 3-14, 9th International conference on Numerical Methods and Applications, NMA 2018, Borovets, Bulgaria, 8/20/18. https://doi.org/10.1007/978-3-030-10692-8_1

New stabilized discretizations for poroelasticity equations. / Gaspar, Francisco J.; Rodrigo, Carmen; Hu, Xiaozhe; Ohm, Peter; Adler, James; Zikatanov, Ludmil.

Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers. ed. / Natalia Kolkovska; Krassimir Georgiev; Geno Nikolov. Springer Verlag, 2019. p. 3-14 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11189 LNCS).

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

TY - GEN

T1 - New stabilized discretizations for poroelasticity equations

AU - Gaspar, Francisco J.

AU - Rodrigo, Carmen

AU - Hu, Xiaozhe

AU - Ohm, Peter

AU - Adler, James

AU - Zikatanov, Ludmil

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85063882873&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063882873&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-10692-8_1

DO - 10.1007/978-3-030-10692-8_1

M3 - Conference contribution

AN - SCOPUS:85063882873

SN - 9783030106911

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 3

EP - 14

BT - Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers

A2 - Kolkovska, Natalia

A2 - Georgiev, Krassimir

A2 - Nikolov, Geno

PB - Springer Verlag

ER -

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