Issue |
ESAIM: M2AN
Volume 57, Number 5, September-October 2023
|
|
---|---|---|
Page(s) | 3007 - 3027 | |
DOI | https://doi.org/10.1051/m2an/2023073 | |
Published online | 29 September 2023 |
A virtual element method for overcoming locking phenomena in Biot’s consolidation model
1
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, P.R. China
2
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada
* Corresponding author: zhachen@ucalgary.ca
Received:
31
October
2022
Accepted:
31
August
2023
A novel algorithm for the three-field formulation of Biot’s consolidation model based on mixed and divergence-free nonconforming virtual element methods is developed and analyzed. By establishing a discrete counterpart of Korn’s inequality, we ensure the well-posedness of this algorithm without special constraints in the context of nonconforming methods. In addition, we also derive a unified error estimate for this fully discrete algorithm no matter whether the specific storage coefficient vanishes or not. Moreover, this algorithm has several features, including supporting general polygonal meshes and arbitrary space approximation orders, and without Poisson’s locking and pressure oscillations. Numerical experiments are presented to validate the performance of this algorithm.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30 / 74F10 / 76S05
Key words: Virtual element method / Biot’s consolidation model / unified error estimate / Poisson locking and pressure oscillation / general polygonal meshes
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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