A comparison of two nonconforming finite element methods for linear three-field poroelasticity
We present and analyze two kinds of nonconforming finite element methods for three-field Biot’s consolidation model in poroelasticity. We employ the Crouzeix-Raviart element for one of the displacement component and conforming linear element for the remaining component, the lowest order Raviart-Thom...
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De Gruyter
2024-12-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2024-0073 |
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| author | Guo Jun Shi Yanchao Luo Weihua |
| author_facet | Guo Jun Shi Yanchao Luo Weihua |
| author_sort | Guo Jun |
| collection | DOAJ |
| description | We present and analyze two kinds of nonconforming finite element methods for three-field Biot’s consolidation model in poroelasticity. We employ the Crouzeix-Raviart element for one of the displacement component and conforming linear element for the remaining component, the lowest order Raviart-Thomas element (or the first-order Brezzi-Douglas-Marini element) for the fluid flux, and the piecewise constant for the pressure. We provide the corresponding analysis, including the well-posedness and a priori error estimates, for the fully discrete scheme coupled with the backward Euler finite difference for the time discretization. Such scheme ensures that the discrete Korn’s inequality is satisfied without adding any stabilization terms. In particular, it is free of poroelasticity locking. Numerical results are presented to compare the accuracy and locking-free performance of the two introduced schemes. |
| format | Article |
| id | doaj-art-1c58e4f2a1b2441a9bb3f1404b8392d6 |
| institution | Kabale University |
| issn | 2391-4661 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-1c58e4f2a1b2441a9bb3f1404b8392d62025-02-02T15:45:16ZengDe GruyterDemonstratio Mathematica2391-46612024-12-0157115516410.1515/dema-2024-0073A comparison of two nonconforming finite element methods for linear three-field poroelasticityGuo Jun0Shi Yanchao1Luo Weihua2College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, P. R. ChinaSchool of Science, Southwest Petroleum University, Chengdu 610500, P. R. ChinaSchool of Mathematics and Physics, Hunan University of Arts and Science, Changde, Hunan 415000, P. R. ChinaWe present and analyze two kinds of nonconforming finite element methods for three-field Biot’s consolidation model in poroelasticity. We employ the Crouzeix-Raviart element for one of the displacement component and conforming linear element for the remaining component, the lowest order Raviart-Thomas element (or the first-order Brezzi-Douglas-Marini element) for the fluid flux, and the piecewise constant for the pressure. We provide the corresponding analysis, including the well-posedness and a priori error estimates, for the fully discrete scheme coupled with the backward Euler finite difference for the time discretization. Such scheme ensures that the discrete Korn’s inequality is satisfied without adding any stabilization terms. In particular, it is free of poroelasticity locking. Numerical results are presented to compare the accuracy and locking-free performance of the two introduced schemes.https://doi.org/10.1515/dema-2024-0073biot’s consolidation modelnonconforming finite element methodporoelasticity lockinglocking-free65n3074s05 |
| spellingShingle | Guo Jun Shi Yanchao Luo Weihua A comparison of two nonconforming finite element methods for linear three-field poroelasticity Demonstratio Mathematica biot’s consolidation model nonconforming finite element method poroelasticity locking locking-free 65n30 74s05 |
| title | A comparison of two nonconforming finite element methods for linear three-field poroelasticity |
| title_full | A comparison of two nonconforming finite element methods for linear three-field poroelasticity |
| title_fullStr | A comparison of two nonconforming finite element methods for linear three-field poroelasticity |
| title_full_unstemmed | A comparison of two nonconforming finite element methods for linear three-field poroelasticity |
| title_short | A comparison of two nonconforming finite element methods for linear three-field poroelasticity |
| title_sort | comparison of two nonconforming finite element methods for linear three field poroelasticity |
| topic | biot’s consolidation model nonconforming finite element method poroelasticity locking locking-free 65n30 74s05 |
| url | https://doi.org/10.1515/dema-2024-0073 |
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