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Volume 42, Issue 4
A Coupled Method Combining Crouzeix-Raviart Nonconforming and Node Conforming Finite Element Spaces for Biot Consolidation Model

Yuping Zeng, Mingchao Cai & Liuqiang Zhong

DOI: 10.4208/jcm.2212-m2021-0231

J. Comp. Math., 42 (2024), pp. 911-931.

Published online: 2024-04

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  • Abstract

A mixed finite element method is presented for the Biot consolidation problem in poroelasticity. More precisely, the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements, while the fluid pressure is approximated by using the node conforming finite elements. The well-posedness of the fully discrete scheme is established, and a corresponding priori error estimate with optimal order in the energy norm is also derived. Numerical experiments are provided to validate the theoretical results.

  • Keywords

Poroelasticity, Nonconforming finite element, Inf-sup condition, A priori error estimate.

  • AMS Subject Headings

65N15, 65M60, 74F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-911, author = {Zeng , YupingCai , Mingchao and Zhong , Liuqiang}, title = {A Coupled Method Combining Crouzeix-Raviart Nonconforming and Node Conforming Finite Element Spaces for Biot Consolidation Model}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {4}, pages = {911--931}, abstract = {

A mixed finite element method is presented for the Biot consolidation problem in poroelasticity. More precisely, the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements, while the fluid pressure is approximated by using the node conforming finite elements. The well-posedness of the fully discrete scheme is established, and a corresponding priori error estimate with optimal order in the energy norm is also derived. Numerical experiments are provided to validate the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2212-m2021-0231}, url = {http://global-sci.org/intro/article_detail/jcm/23040.html} }
TY - JOUR T1 - A Coupled Method Combining Crouzeix-Raviart Nonconforming and Node Conforming Finite Element Spaces for Biot Consolidation Model AU - Zeng , Yuping AU - Cai , Mingchao AU - Zhong , Liuqiang JO - Journal of Computational Mathematics VL - 4 SP - 911 EP - 931 PY - 2024 DA - 2024/04 SN - 42 DO - http://doi.org/10.4208/jcm.2212-m2021-0231 UR - https://global-sci.org/intro/article_detail/jcm/23040.html KW - Poroelasticity, Nonconforming finite element, Inf-sup condition, A priori error estimate. AB -

A mixed finite element method is presented for the Biot consolidation problem in poroelasticity. More precisely, the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements, while the fluid pressure is approximated by using the node conforming finite elements. The well-posedness of the fully discrete scheme is established, and a corresponding priori error estimate with optimal order in the energy norm is also derived. Numerical experiments are provided to validate the theoretical results.

Yuping Zeng, Mingchao Cai & Liuqiang Zhong. (2024). A Coupled Method Combining Crouzeix-Raviart Nonconforming and Node Conforming Finite Element Spaces for Biot Consolidation Model. Journal of Computational Mathematics. 42 (4). 911-931. doi:10.4208/jcm.2212-m2021-0231
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