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On stability and convergence of finite element approximations of Biot’s consolidation problem. (English) Zbl 0791.76047

Summary: Stability and convergence analysis of finite element approximations of Biot’s equations governing quasi-static 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.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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