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 | |
| State | Published - Jan 1 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 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
}
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
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 -