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

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 L2L2-norm are proved. Numerical examples are given to illustrate the good performance of the proposed numerical approach.