Staggered grid discretizations for the quasi-static Biot's consolidation problem

Finite difference methods for a two-dimensional quasi-static Biot's consolidation problem are considered. Stabilized space discretization using staggered grids and the implicit Euler scheme for time stepping is proposed. A priori estimates for displacements and pressure in discrete energy norms are obtained and the corresponding convergence results are proved. Numerical examples are given to illustrate the convergence properties of these stabilized methods.