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On stability and convergence of finite element approximations of Biot's consolidation problem
Author(s) -
Murad Márcio A.,
Loula Abimael F. D.
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620370407
Subject(s) - biot number , quasistatic process , consolidation (business) , finite element method , mathematics , galerkin method , mathematical analysis , convergence (economics) , euler's formula , porous medium , porosity , physics , mechanics , geotechnical engineering , geology , accounting , quantum mechanics , economics , business , thermodynamics , economic growth
Stability 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.