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
N1 - Funding Information:
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.
Funding Information:
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.
Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019
Y1 - 2019
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.
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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
T2 - 9th International conference on Numerical Methods and Applications, NMA 2018
Y2 - 20 August 2018 through 24 August 2018
ER -