Numerical methods for a one-dimensional non-linear Biot's model

被引:6
作者
Gaspar, Francisco J. [1 ]
Lisbona, Francisco J. [1 ]
Matus, Piotr [2 ,3 ]
Vo Thi Kim Tuyen [4 ]
机构
[1] Univ Zaragoza, Dept Appl Math, E-50009 Zaragoza, Spain
[2] John Paul II Catholic Univ Lublin, Inst Math & Comp Sci, PL-20950 Lublin, Poland
[3] NAS Belarus, Inst Math, Minsk 20072, BELARUS
[4] Belarusian State Univ, Minsk 220030, BELARUS
关键词
Finite-difference scheme; Maximum principle; Non-linear Blot's model; FINITE-DIFFERENCE ANALYSIS; EXISTENCE-UNIQUENESS; CONSOLIDATION; DISCRETIZATIONS;
D O I
10.1016/j.cam.2015.03.039
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Staggered finite difference methods for a one-dimensional Biot's problem are considered. The permeability tensor of the porous medium is assumed to depend on the strain, thus yielding a non-linear model. Some strong two-side estimates for displacements and for pressure are provided and convergence results in the discrete L-2-norm are proved. Numerical examples are given to illustrate the good performance of the proposed numerical approach. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码:62 / 72
页数:11
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