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Volume 16, Issue 3
The MFE-CFE-GFE Method for the Fully Coupled Quasi-Static Thermo-Poroelastic Problem

Jing Zhang & Hongxing Rui

DOI: 10.4208/nmtma.OA-2022-0143

Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 792-819.

Published online: 2023-08

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  • Abstract

In this work, we consider a combined finite element method for fully coupled nonlinear thermo-poroelastic model problems. The mixed finite element (MFE) method is used for the pressure, the characteristics finite element (CFE) method is used for the temperature, and the Galerkin finite element (GFE) method is used for the elastic displacement. The semi-discrete and fully discrete finite element schemes are established and the stability of this method is presented. We derive error estimates for the pressure, temperature and displacement. Several numerical examples are presented to confirm the accuracy of the method.

  • Keywords

Quasi-static thermo-poroelasticity, characteristics finite element method, porous media, numerical experiments.

  • AMS Subject Headings

35M10, 65M12, 65M60, 74F05, 74F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-16-792, author = {Zhang , Jing and Rui , Hongxing}, title = {The MFE-CFE-GFE Method for the Fully Coupled Quasi-Static Thermo-Poroelastic Problem}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {3}, pages = {792--819}, abstract = {

In this work, we consider a combined finite element method for fully coupled nonlinear thermo-poroelastic model problems. The mixed finite element (MFE) method is used for the pressure, the characteristics finite element (CFE) method is used for the temperature, and the Galerkin finite element (GFE) method is used for the elastic displacement. The semi-discrete and fully discrete finite element schemes are established and the stability of this method is presented. We derive error estimates for the pressure, temperature and displacement. Several numerical examples are presented to confirm the accuracy of the method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0143}, url = {http://global-sci.org/intro/article_detail/nmtma/21967.html} }
TY - JOUR T1 - The MFE-CFE-GFE Method for the Fully Coupled Quasi-Static Thermo-Poroelastic Problem AU - Zhang , Jing AU - Rui , Hongxing JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 792 EP - 819 PY - 2023 DA - 2023/08 SN - 16 DO - http://doi.org/10.4208/nmtma.OA-2022-0143 UR - https://global-sci.org/intro/article_detail/nmtma/21967.html KW - Quasi-static thermo-poroelasticity, characteristics finite element method, porous media, numerical experiments. AB -

In this work, we consider a combined finite element method for fully coupled nonlinear thermo-poroelastic model problems. The mixed finite element (MFE) method is used for the pressure, the characteristics finite element (CFE) method is used for the temperature, and the Galerkin finite element (GFE) method is used for the elastic displacement. The semi-discrete and fully discrete finite element schemes are established and the stability of this method is presented. We derive error estimates for the pressure, temperature and displacement. Several numerical examples are presented to confirm the accuracy of the method.

Jing Zhang & Hongxing Rui. (2023). The MFE-CFE-GFE Method for the Fully Coupled Quasi-Static Thermo-Poroelastic Problem. Numerical Mathematics: Theory, Methods and Applications. 16 (3). 792-819. doi:10.4208/nmtma.OA-2022-0143
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