Year: 2019
Author: Luoping Chen, Yanping Chen
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 6 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0003
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 6 : pp. 1339–1357
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Poroelasticity problem finite element method multigrid method.