Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S909 - S939|
|Published online||26 February 2021|
On the locking-free three-field virtual element methods for Biot’s consolidation model in poroelasticity
Southwest Petroleum University State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu 610500, P.R. China
2 Chengdu North Petroleum Exploration and Development Technology Company Limited, Chengdu 610051, P.R. China
3 College of Mathematics, Sichuan University, Chengdu 610065, P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 28 August 2020
We propose and analyze two locking-free three-field virtual element methods for Biot’s consolidation model in poroelasticity. One is a high-order scheme, and the other is a low-order scheme. For time discretization, we use the backward Euler scheme. The proposed methods are well-posed, and optimal error estimates of all the unknowns are obtained for fully discrete solutions. The generic constants in the estimates are uniformly bounded as the Lamé coefficient λ tends to infinity, and as the constrained specific storage coefficient is arbitrarily small. Therefore the methods are free of both Poisson locking and pressure oscillations. Numerical results illustrate the good performance of the methods and confirm our theoretical predictions.
Mathematics Subject Classification: 65M12 / 65M60
Key words: Virtual elements / poroelasticity / Biot’s consolidation model / locking-free / pressure oscillations
© EDP Sciences, SMAI 2021
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