Volume 12, Issue 6
A New Mixed Finite Element Method for Biot Consolidation Equations

Adv. Appl. Math. Mech., 12 (2020), pp. 1520-1541.

Published online: 2020-09

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• Abstract

In this paper, we study a new finite element method for poroelasticity problem with homogeneous boundary conditions. The finite element discretization method is based on a three-variable weak form with mixed finite element for the linear elasticity, i.e., the stress tensor, displacement and pressure are unknown variables in the weak form. For the linear elasticity formula, we use a conforming finite element proposed in [11] for the mixed form of the linear elasticity and piecewise continuous finite element for the pressure of the fluid flow. We will show that the newly proposed finite element method maintains optimal convergence order.

• Keywords

Biot consolidation equations, linear elasticity, finite element method, convergence analysis.

65M10, 78A48

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@Article{AAMM-12-1520, author = {Chen , Luoping and Yang , Yan}, title = {A New Mixed Finite Element Method for Biot Consolidation Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {6}, pages = {1520--1541}, abstract = {

In this paper, we study a new finite element method for poroelasticity problem with homogeneous boundary conditions. The finite element discretization method is based on a three-variable weak form with mixed finite element for the linear elasticity, i.e., the stress tensor, displacement and pressure are unknown variables in the weak form. For the linear elasticity formula, we use a conforming finite element proposed in [11] for the mixed form of the linear elasticity and piecewise continuous finite element for the pressure of the fluid flow. We will show that the newly proposed finite element method maintains optimal convergence order.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0174}, url = {http://global-sci.org/intro/article_detail/aamm/18298.html} }
TY - JOUR T1 - A New Mixed Finite Element Method for Biot Consolidation Equations AU - Chen , Luoping AU - Yang , Yan JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1520 EP - 1541 PY - 2020 DA - 2020/09 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0174 UR - https://global-sci.org/intro/article_detail/aamm/18298.html KW - Biot consolidation equations, linear elasticity, finite element method, convergence analysis. AB -

In this paper, we study a new finite element method for poroelasticity problem with homogeneous boundary conditions. The finite element discretization method is based on a three-variable weak form with mixed finite element for the linear elasticity, i.e., the stress tensor, displacement and pressure are unknown variables in the weak form. For the linear elasticity formula, we use a conforming finite element proposed in [11] for the mixed form of the linear elasticity and piecewise continuous finite element for the pressure of the fluid flow. We will show that the newly proposed finite element method maintains optimal convergence order.

Luoping Chen & Yan Yang. (2020). A New Mixed Finite Element Method for Biot Consolidation Equations. Advances in Applied Mathematics and Mechanics. 12 (6). 1520-1541. doi:10.4208/aamm.OA-2019-0174
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