Finite element analysis of poro-elastic consolidation in porous media: Standard and mixed approaches

In this paper two different numerical approaches for consolidation in porous media are developed and thoroughly compared: Galerkin finite element method (GFEM) and least-squares mixed finite element methods (LS-MFEM). The primary variables of the GFEM are fluid pressure and solid displacement. Fluid fluxes and stresses are derived quantities. In the LS-MFEM method all four unknown functions are primary variables, which results in more accurate approximations of fluid fluxes and stresses. Results of both numerical methods are compared for two examples. The first example, for which an analytical solution is known, is used in order to verify the implementation of the numerical schemes. In the second example, for a footing problem which was proposed by Murad et al. [M. Murad, V. Thomée, A. Loula, Asymptotic behavior of semidiscrete finite-element approximations of Biot’s consolidation problem, SIAM J. Numer. Anal., 33 (1996) 1065–1083], a detailed numerical analysis and comparison of both schemes are presented.