New stabilized discretizations for poroelasticity equations

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

doi:10.1007/978-3-030-10692-8_1

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 proceeding › Conference 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 language	English (US)
Title of host publication	Numerical Methods and Applications - 9th International Conference, NMA 2018, Revised Selected Papers
Editors	Natalia Kolkovska, Krassimir Georgiev, Geno Nikolov
Publisher	Springer Verlag
Pages	3-14
Number of pages	12
ISBN (Print)	9783030106911
DOIs	https://doi.org/10.1007/978-3-030-10692-8_1
State	Published - 2019
Event	9th International conference on Numerical Methods and Applications, NMA 2018 - Borovets, Bulgaria Duration: Aug 20 2018 → Aug 24 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11189 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	9th International conference on Numerical Methods and Applications, NMA 2018
Country	Bulgaria
City	Borovets
Period	8/20/18 → 8/24/18

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

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

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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)).

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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 proceeding › Conference contribution

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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.

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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