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New Stabilized Discretizations for Poroelasticity Equations

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Numerical Methods and Applications (NMA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11189))

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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.

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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.

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Authors and Affiliations

  1. Centrum Wiskunde & Informatica (CWI), Science Park 123, 1090, Amsterdam, The Netherlands

    Francisco J. Gaspar

  2. IUMA and Department of Applied Mathematics, University of Zaragoza, Zaragoza, Spain

    Carmen Rodrigo

  3. Department of Mathematics, Tufts University, Medford, MA, 02155, USA

    Xiaozhe Hu, Peter Ohm & James Adler

  4. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Ludmil Zikatanov

Authors
  1. Francisco J. Gaspar
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  2. Carmen Rodrigo
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  3. Xiaozhe Hu
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  4. Peter Ohm
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  5. James Adler
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  6. Ludmil Zikatanov
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Corresponding author

Correspondence to Francisco J. Gaspar .

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Editors and Affiliations

  1. Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria

    Geno Nikolov

  2. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Natalia Kolkovska

  3. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir Georgiev

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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: Nikolov, G., Kolkovska, N., Georgiev, K. (eds) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science(), vol 11189. Springer, Cham. https://doi.org/10.1007/978-3-030-10692-8_1

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  • DOI: https://doi.org/10.1007/978-3-030-10692-8_1

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  • Online ISBN: 978-3-030-10692-8

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