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A FIC‐based stabilized mixed finite element method with equal order interpolation for solid–pore fluid interaction problems
Author(s) -
dePouplana Ignasi,
Oñate Eugenio
Publication year - 2017
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2550
Subject(s) - interpolation (computer graphics) , finite element method , displacement (psychology) , mathematics , mathematical analysis , linear interpolation , calculus (dental) , physics , classical mechanics , thermodynamics , motion (physics) , psychology , medicine , dentistry , polynomial , psychotherapist
Summary A new mixed displacement‐pressure element for solving solid–pore fluid interaction problems is presented. In the resulting coupled system of equations, the balance of momentum equation remains unaltered, while the mass balance equation for the pore fluid is stabilized with the inclusion of higher‐order terms multiplied by arbitrary dimensions in space, following the finite calculus (FIC) procedure. The stabilized FIC‐FEM formulation can be applied to any kind of interpolation for the displacements and the pressure, but in this work, we have used linear elements of equal order interpolation for both set of unknowns. Examples in 2D and 3D are presented to illustrate the accuracy of the stabilized formulation for solid–pore fluid interaction problems. Copyright © 2016 John Wiley & Sons, Ltd.