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

Francisco J. Gaspar ^[1] ; Francisco J. Lisbona ^[1] ; Piotr Matus ^[2] ; Vo Thi Kim Tuyen ^[3]
1. [1] Universidad de Zaragoza
  
  Universidad de Zaragoza
  
  Zaragoza, España
2. [2] John Paul II Catholic University of Lublin
  
  John Paul II Catholic University of Lublin
  
  Lublin, Polonia
3. [3] Belarusian State University
  
  Belarusian State University
  
  Bielorrusia
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Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 293, Nº 1 (February 2016), 2016, págs. 62-72
Idioma: inglés
DOI: 10.1016/j.cam.2015.03.039
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Resumen
- 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 L2-norm are proved. Numerical examples are given to illustrate the good performance of the proposed numerical approach.