A nonconforming finite element method for the Biot's consolidation model in poroelasticity

被引：67

作者：

Hu, Xiaozhe ^{[1
]}

Rodrigo, Carmen ^{[2
]}

Gaspar, Francisco J. ^{[2
]}

Zikatanov, Ludmil T. ^{[3
,4
]}

机构：

[1] Tufts Univ, Dept Math, Medford, MA 02155 USA

[2] Univ Zaragoza, Dept Matemat Aplicada, E-50009 Zaragoza, Spain

[3] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[4] Bulgarian Acad Sci, Inst Math & Informat, Sofia, Bulgaria

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2017年 / 310卷

基金：

美国国家科学基金会;

关键词：

Nonconforming finite elements; Stable discretizations; Monotone discretizations; Poroelasticity; LINEAR ELASTICITY; APPROXIMATIONS; STABILITY; EQUATIONS;

D O I：

10.1016/j.cam.2016.06.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A stable finite element scheme that avoids pressure oscillations for a three-field Biot's model in poroelasticity is considered. The involved variables are the displacements, fluid flux (Darcy velocity), and the pore pressure, and they are discretized by using the lowest possible approximation order: Crouzeix-Raviart finite elements for the displacements,. lowest order Raviart-Thomas-Nedelec elements for the Darcy velocity, and piecewise constant approximation for the pressure. Mass-lumping technique is introduced for the Raviart-Thomas-Nedelec elements in order to eliminate the Darcy velocity and, therefore, reduce the computational cost. We show convergence of the discrete scheme which is implicit in time and use these types of elements in space with and without mass lumping. Finally, numerical experiments illustrate the convergence of the method and show its effectiveness to avoid spurious pressure oscillations when mass lumping for the Raviart-Thomas-Nedelec elements is used. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：143 / 154

页数：12

共 42 条

[1] Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation [J].