A Galerkin/least-squares finite element formulation for consolidation

A Galerkin=least-squares (GLS) .nite element formulation for problem of consolidation of fully saturated two-phase media is presented. The elimination of spurious pressure oscillations appearing at the early stage of consolidation for standard Galerkin .nite elements with equal interpolation order for both displacements and pressures is the goal of the approach. It will be shown that the least-squares term, based exclusively on the residuumof the =uid =ow continuity equation, added to the standard Galerkin formulation enhances its stability and can fully eliminate pressure oscillations. A reasonably simple framework designed for derivation of one-dimensional as well as multi-dimensional estimates of the stabilization factor is proposed and then veri.ed. The formulation is validated on one-dimensional and then on two-dimensional, linear and non-linear test problems. The e?ect of the =uid incompressibility as well as compressibility will be taken into account and investigated