Lahorarorio Nocional de Compuraccio Cientifica 1,NCCJCNPq Rua b u r 0 Muller 455, 222W-Rio de Juneiro,
Brazil
S U M MARYStability and convergence analysis of finite element approximations of Biot's equations governing quasistatic consolidation of saturated porous media are discussed. A family of decay functions, parametrized by the number of time steps, is derived for the fully discrete backward Euler--Galerkin formulation, showing that the pore-pressure oscillations, arising from an unstable approximation of the incompressibility constraint on the initial condition, decay in time. Error estimates holding over the unbounded time domain for both semidiscrete and fully discrete formulations are presented, and a post-processing technique is employed to improve the pore-pressure accuracy.
Summary. Adding to the classical Hellinger Reissner formulation another residual form of the equilibrium equation, a new Petrov-Galerkin finite element method is derived. It fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations, including equal-order discontinuous stress and continuous displacement interpolations which are unstable within the Galerkin approach. Error estimates are presented using the Babugka-Brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method.
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