Analysis of finite element methods for dynamic poroelasticity: Low frequency waves

被引:0
作者
Lee, Jeonghun J. [1 ]
机构
[1] Baylor Univ, Dept Math, Sid Richardson Sci Bldg,One Bear,Pl 97328, Waco, TX 76798 USA
关键词
Poroelasticity; Finite element method; Error analysis; BIOTS CONSOLIDATION MODEL; DISCONTINUOUS GALERKIN; ELASTICITY ELEMENT; LINEAR ELASTICITY; MIXED METHODS; POROUS-MEDIA; PROPAGATION; BEHAVIOR; APPROXIMATIONS; CONVERGENCE;
D O I
10.1016/j.cam.2022.114717
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we consider a finite element discretization of low-frequency dynamic poroelasticity models and carry out the a priori error analysis. In contrast to the widely used quasi-static poroelasticity models, the dynamic models are hyperbolic partial differential equations with acceleration terms of solid and fluid phases. We reformulate the problem to a symmetric hyperbolic system and discretize it with two mixed finite element methods. The error analysis semidiscrete solutions are discussed in detail and numerical results of the backward Euler fully discrete scheme are presented. (C) 2022 Elsevier B.V. All rights reserved.
引用
收藏
页数:12
相关论文
共 50 条
[41]   Error Analysis of Mixed Finite Element Methods for Nonlinear Parabolic Equations [J].
Gao, Huadong ;
Qiu, Weifeng .
JOURNAL OF SCIENTIFIC COMPUTING, 2018, 77 (03) :1660-1678
[42]   A stabilized hybrid mixed finite element method for poroelasticity [J].
Chunyan Niu ;
Hongxing Rui ;
Xiaozhe Hu .
Computational Geosciences, 2021, 25 :757-774
[43]   Numerical analysis of frost effects in porous media. Benefits and limits of the finite element poroelasticity formulation [J].
Multon, Stephane ;
Sellier, Alain ;
Perrin, Bernard .
INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, 2012, 36 (04) :438-458
[44]   A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case [J].
Phillips, Phillip Joseph ;
Wheeler, Mary F. .
COMPUTATIONAL GEOSCIENCES, 2007, 11 (02) :131-144
[45]   Finite element methods: Research in India over the last decade [J].
Nataraj, Neela ;
Murthy, A. S. Vasudeva .
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2019, 50 (03) :739-765
[46]   A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case [J].
Phillip Joseph Phillips ;
Mary F. Wheeler .
Computational Geosciences, 2007, 11
[47]   Multigrid Method for Poroelasticity Problem by Finite Element Method [J].
Chen, Luoping ;
Chen, Yanping .
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2019, 11 (06) :1339-1357
[48]   A stabilized hybrid mixed finite element method for poroelasticity [J].
Niu, Chunyan ;
Rui, Hongxing ;
Hu, Xiaozhe .
COMPUTATIONAL GEOSCIENCES, 2021, 25 (02) :757-774
[49]   Large scale micro finite element analysis of 3D bone poroelasticity [J].
Turan, Erhan ;
Arbenz, Peter .
PARALLEL COMPUTING, 2014, 40 (07) :239-250
[50]   Robust a posteriori error estimation for mixed finite element approximation of linear poroelasticity [J].
Khan, Arbaz ;
Silvester, David J. .
IMA JOURNAL OF NUMERICAL ANALYSIS, 2021, 41 (03) :2000-2025