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Quasilinear poroelasticity: Analysis and hybrid finite element approximation
Authors:Yanzhao Cao  Song Chen  A J Meir
Institution:1. Department of Mathematics and Statistics, Auburn University, Auburn, Alabama;2. Department of Mathematics, University of Wisconsin‐La Crosse, La Crosse, Wisconsin
Abstract: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 has urn:x-wiley:0749159X:media:num21940:num21940-math-0001 regularity. 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
Keywords:poroelasticity  finite elements  least squares
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