Finite difference schemes for poro-elastic problems

Abstract

In this paper, we present a finite difference analysis of the consolidation problem for saturated porous media. In the classical model, the behaviour of the porous environment — fluid system is described by a set of equations for the unknown vector displacements of the matrix skeleton and the fluid pressure. For simplicity we consider a model problem with constant coefficients in a rectangular domain. A priori estimates for the difference solution of the problem are obtained and on their basis the convergence of two-level difference schemes is investigated. © 2002, Institute of Mathematics, NAS of Belarus. All rights reserved.