Quasilinear poroelasticity: Analysis and hybrid finite element approximation
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 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
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 20, 2014
- Source ID
- 10.1002/num.21940
Entities
People
- A. J. Meir
- Song Chen
- Yanzhao Cao
Organizations
- Air Force Office of Scientific Research
- Auburn University
- National Science Foundation
- University of Wisconsin–La Crosse