Volume 11, Issue 6
Multigrid Method for Poroelasticity Problem by Finite Element Method

Adv. Appl. Math. Mech., 11 (2019), pp. 1339-1357.

Published online: 2019-09

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• Abstract

In this paper, we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional space. We choose Nédélec edge element for the displacement variable and piecewise continuous polynomials for the pressure variable in the model problem. In constructing multigrid algorithm, a distributive Gauss-Seidel iteration method is applied. Numerical experiments shows that the finite element method achieves optimal convergence order and the multigrid algorithm is almost uniformly convergent to mesh size $h$ and parameter $\delta t$ on regular meshes.

• Keywords

Poroelasticity problem, finite element method, multigrid method.

65M10, 78A48

cherrychen@home.swjtu.edu.cn (Luoping Chen)

yanpingchen@scnu.edu.cn (Yanping Chen)

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@Article{AAMM-11-1339, author = {Luoping and Chen and cherrychen@home.swjtu.edu.cn and 5174 and School of Mathematics, Southwest Jiaotong University, Chengdu 611756, Sichuan, China and Luoping Chen and Yanping and Chen and yanpingchen@scnu.edu.cn and 10877 and School of Mathematical Sciences, South China Normal University, Guangzhou, China and Yanping Chen}, title = {Multigrid Method for Poroelasticity Problem by Finite Element Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {6}, pages = {1339--1357}, abstract = {

In this paper, we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional space. We choose Nédélec edge element for the displacement variable and piecewise continuous polynomials for the pressure variable in the model problem. In constructing multigrid algorithm, a distributive Gauss-Seidel iteration method is applied. Numerical experiments shows that the finite element method achieves optimal convergence order and the multigrid algorithm is almost uniformly convergent to mesh size $h$ and parameter $\delta t$ on regular meshes.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0003}, url = {http://global-sci.org/intro/article_detail/aamm/13306.html} }
TY - JOUR T1 - Multigrid Method for Poroelasticity Problem by Finite Element Method AU - Chen , Luoping AU - Chen , Yanping JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1339 EP - 1357 PY - 2019 DA - 2019/09 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2019-0003 UR - https://global-sci.org/intro/article_detail/aamm/13306.html KW - Poroelasticity problem, finite element method, multigrid method. AB -

In this paper, we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional space. We choose Nédélec edge element for the displacement variable and piecewise continuous polynomials for the pressure variable in the model problem. In constructing multigrid algorithm, a distributive Gauss-Seidel iteration method is applied. Numerical experiments shows that the finite element method achieves optimal convergence order and the multigrid algorithm is almost uniformly convergent to mesh size $h$ and parameter $\delta t$ on regular meshes.

Luoping Chen & Yanping Chen. (2019). Multigrid Method for Poroelasticity Problem by Finite Element Method. Advances in Applied Mathematics and Mechanics. 11 (6). 1339-1357. doi:10.4208/aamm.OA-2019-0003
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