Applied Numerical Mathematics 44 (2003) 487–506 www.elsevier.com/locate/apnum A finite difference analysis of Biot’s consolidation model ✩ F.J. Gaspar a , F.J. Lisbona a,∗ , P.N. Vabishchevich b a Departamento de Matemática Aplicada, University of Zaragoza, Zaragoza, Spain b Institute for Mathematical Modelling RAS 4-A. Miusskaya Sq. 124047, Moscow, Russia Abstract In this paper, stability estimates and convergence analysis of finite difference methods for the Biot’s consolidation model are presented. Initially central differences for space discretization and a weighed two-level time scheme are analyzed. To improve some stability and convergence limitations for this scheme we also consider space discretizations on MAC type grids (staggered grids). Numerical results are given to illustrate the obtained theoretical results.  2002 IMACS. Published by Elsevier Science B.V. All rights reserved. Keywords: Biot’s model; Finite-differences; MAC grids 1. Introduction We deal with the numerical approximation of the classical Biot consolidation problem for a saturated, homogeneous, isotropic, porous medium composed of an incompressible solid matrix. The classical quasi-static Biot model is obtained in [2–4] for incompressible fluids, but on the assumption that the soil is not completely saturated. The same equations are used by Bear and Bachmat [1] to model the case of slightly compressible fluids in a totally saturated porous medium, with a different meaning of the γ parameter in Eq. (2). Neglecting body forces, the filtration and consolidation problem is governed by the set of equations -µu - (λ + µ) grad div u + grad p = 0, (1) ∂ ∂t (γp + div u) - κ η p = f(x ,t), x ∈ Ω, 0 <t  T, (2) ✩ This research has been partially supported by the Spanish project MCYT-FEDER BFM 2001-2521 and the Russian Foundation for Basic Research RFBR 99-01-00958. * Corresponding author. E-mail address: lisbona@posta.unizar.es (F.J. Lisbona). 0168-9274/02/$30.00  2002 IMACS. Published by Elsevier Science B.V. All rights reserved. PII:S0168-9274(02)00190-3