ON STABILITY AND CONVERGENCE OF FINITE-ELEMENT APPROXIMATIONS OF BIOTS CONSOLIDATION PROBLEM

Stability and convergence analysis of finite element approximations of Blot's equations governing quasistatic consolidation of saturated por ous media are discussed. A family of decay functions, parametrized by the number of time steps, is derived for the fully discrete backward E uler-Galerkin formulation, showing that the pore-pressure oscillations , arising from an unstable approximation of the incompressibility cons traint on the initial condition, decay in time. Error estimates holdin g over the unbounded time domain for both semidiscrete and fully discr ete formulations are presented, and a post-processing technique is emp loyed to improve the pore-pressure accuracy.