An Accuracy Condition for the Finite Element Discretization of Biot's Equations on Triangular Meshes

Marco Favino; Jürg Hunziker; Klaus Holliger; Rolf Krause

doi:10.1061/9780784480779.021

An Accuracy Condition for the Finite Element Discretization of Biot's Equations on Triangular Meshes

Marco Favino, Jürg Hunziker, Klaus Holliger, Rolf Krause

Applied Mathematics and Computational Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

Finite element solutions of Biot's equations may be characterized by unphysical oscillations for small time-steps or low permeabilities. We analyse these numerical wiggles by comparing the Schur complement of the system with an equivalent reaction-diffusion problem. We show that the non-physical behaviour of the discrete solution is due to the fact that the discrete maximum principle is not satisfied. We provide a sufficient condition for two-dimensional problems of this kind to ensure monotonic solutions on triangular meshes.

Original language	English (US)
Title of host publication	Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics
Editors	Patrick Dangla, Jean-Michel Pereira, Siavash Ghabezloo, Matthieu Vandamme
Publisher	American Society of Civil Engineers (ASCE)
Pages	172-181
Number of pages	10
ISBN (Electronic)	9780784480779
DOIs	https://doi.org/10.1061/9780784480779.021
State	Published - 2017
Event	6th Biot Conference on Poromechanics, Poromechanics 2017 - Paris, France Duration: Jul 9 2017 → Jul 13 2017

Publication series

Name	Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics

Other

Other	6th Biot Conference on Poromechanics, Poromechanics 2017
Country/Territory	France
City	Paris
Period	07/9/17 → 07/13/17

Bibliographical note

Publisher Copyright:
© ASCE.

ASJC Scopus subject areas

Condensed Matter Physics
Mechanics of Materials
Acoustics and Ultrasonics

Access to Document

10.1061/9780784480779.021

Cite this

Favino, M., Hunziker, J., Holliger, K., & Krause, R. (2017). An Accuracy Condition for the Finite Element Discretization of Biot's Equations on Triangular Meshes. In P. Dangla, J.-M. Pereira, S. Ghabezloo, & M. Vandamme (Eds.), Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics (pp. 172-181). (Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics). American Society of Civil Engineers (ASCE). https://doi.org/10.1061/9780784480779.021

Favino, Marco ; Hunziker, Jürg ; Holliger, Klaus et al. / An Accuracy Condition for the Finite Element Discretization of Biot's Equations on Triangular Meshes. Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics. editor / Patrick Dangla ; Jean-Michel Pereira ; Siavash Ghabezloo ; Matthieu Vandamme. American Society of Civil Engineers (ASCE), 2017. pp. 172-181 (Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics).

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abstract = "Finite element solutions of Biot's equations may be characterized by unphysical oscillations for small time-steps or low permeabilities. We analyse these numerical wiggles by comparing the Schur complement of the system with an equivalent reaction-diffusion problem. We show that the non-physical behaviour of the discrete solution is due to the fact that the discrete maximum principle is not satisfied. We provide a sufficient condition for two-dimensional problems of this kind to ensure monotonic solutions on triangular meshes.",

author = "Marco Favino and J{\"u}rg Hunziker and Klaus Holliger and Rolf Krause",

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Favino, M, Hunziker, J, Holliger, K & Krause, R 2017, An Accuracy Condition for the Finite Element Discretization of Biot's Equations on Triangular Meshes. in P Dangla, J-M Pereira, S Ghabezloo & M Vandamme (eds), Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics. Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics, American Society of Civil Engineers (ASCE), pp. 172-181, 6th Biot Conference on Poromechanics, Poromechanics 2017, Paris, France, 07/9/17. https://doi.org/10.1061/9780784480779.021

An Accuracy Condition for the Finite Element Discretization of Biot's Equations on Triangular Meshes. / Favino, Marco; Hunziker, Jürg; Holliger, Klaus et al.
Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics. ed. / Patrick Dangla; Jean-Michel Pereira; Siavash Ghabezloo; Matthieu Vandamme. American Society of Civil Engineers (ASCE), 2017. p. 172-181 (Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Finite element solutions of Biot's equations may be characterized by unphysical oscillations for small time-steps or low permeabilities. We analyse these numerical wiggles by comparing the Schur complement of the system with an equivalent reaction-diffusion problem. We show that the non-physical behaviour of the discrete solution is due to the fact that the discrete maximum principle is not satisfied. We provide a sufficient condition for two-dimensional problems of this kind to ensure monotonic solutions on triangular meshes.

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Favino M, Hunziker J, Holliger K, Krause R. An Accuracy Condition for the Finite Element Discretization of Biot's Equations on Triangular Meshes. In Dangla P, Pereira JM, Ghabezloo S, Vandamme M, editors, Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics. American Society of Civil Engineers (ASCE). 2017. p. 172-181. (Poromechanics 2017 - Proceedings of the 6th Biot Conference on Poromechanics). doi: 10.1061/9780784480779.021

An Accuracy Condition for the Finite Element Discretization of Biot's Equations on Triangular Meshes

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