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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:293

Article

Gaspar, Francisco J.¹  Lisbona, Francisco J.¹  Matus, Piotr^2,3  Vo Thi Kim Tuyen⁴ 

[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;   

DOI  :  10.1016/j.cam.2015.03.039

来源: Elsevier

【 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.

【 授权许可】

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