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

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 293卷

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

页码：62 / 72

页数：11

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