Weak Galerkin method for the Biot's consolidation model

被引：31

作者：

Hu, Xiaozhe ^{[1
]}

Mu, Lin ^{[2
]}

Ye, Xiu ^{[3
]}

机构：

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

[2] Oak Ridge Natl Lab, Comp Sci & Math Div, Oak Ridge, TN 37831 USA

[3] Univ Arkansas, Dept Math & Stat, Little Rock, AR 72204 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 75卷 / 06期

基金：

美国国家科学基金会;

关键词：

Biot's consolidation model; Finite element method; Weak Galerkin finite elements method; FINITE-ELEMENT-METHOD; POROELASTICITY; CONVERGENCE; FLOW; DISCRETIZATIONS; APPROXIMATIONS; ELASTICITY; STABILITY; SOIL;

D O I：

10.1016/j.camwa.2017.07.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a weak Galerkin (WG) finite element method for the Biot's consolidation model in the classical displacement-pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure without special treatment. Numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：2017 / 2030

页数：14

共 54 条

[11]

Dautov R.Z., 1997, DIFF URAVN, V33, P515

[12] On convergence of certain finite volume difference discretizations for 1D poroelasticity interface problems [J].