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Quasilinear poroelasticity: Analysis and hybrid finite element approximation
Author(s) -
Cao Yanzhao,
Chen Song,
Meir A. J.
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21940
Subject(s) - poromechanics , finite element method , mathematics , elasticity (physics) , partial differential equation , partial derivative , mathematical analysis , porous medium , displacement (psychology) , linear elasticity , mixed finite element method , porosity , physics , materials science , psychology , composite material , psychotherapist , thermodynamics
We consider a system of partial differential equations which models flows through elastic porous media. This system consists of an elasticity equation describing the displacement of an elastic porous matrix and a quasilinear elliptic equation describing the pressure of the saturating fluid (flowing through its pores). In this model, the permeability depends nonlinearly on the dilatation (divergence of the displacement) of the medium. We show that the solution hasW m 2regularity. We describe the numerical approximation of solutions using a hybrid finite element‐least squares mixed finite element method. Error estimates are obtained through the introduction of an auxiliary linear elasticity equation. Numerical experiments verify the error estimates and validate the proposed poroelasticity model. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1174–1189, 2015