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Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation
Author(s) -
Aguilar G.,
Gaspar F.,
Lisbona F.,
Rodrigo C.
Publication year - 2008
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.2295
Subject(s) - biot number , discretization , poromechanics , mathematics , perturbation (astronomy) , consolidation (business) , finite element method , mathematical analysis , piecewise , piecewise linear function , numerical analysis , mechanics , physics , porous medium , materials science , porosity , thermodynamics , composite material , accounting , quantum mechanics , business
In this paper a stabilized finite element scheme for the poroelasticity equations is proposed. This method, based on the perturbation of the flow equation, allows us to use continuous piecewise linear approximation spaces for both displacements and pressure, obtaining solutions without oscillations independently of the chosen discretization parameters. The perturbation term depends on a parameter which is established in terms of the mesh size and the properties of the material. In the one‐dimensional case, this parameter is shown to be optimal. Some numerical experiments are presented indicating the efficiency of the proposed stabilization technique. Copyright © 2008 John Wiley & Sons, Ltd.