Finite Element Formulation for a Poroelasticity Problem Stemming from Mixture Theory

TL;DR

This paper develops a finite element method for modeling fluid flow in poroelastic media like brain tissue, based on mixture theory, with a focus on stability, convergence, and numerical validation.

Contribution

It introduces a novel finite element formulation for poroelasticity derived from mixture theory, using an ALE perspective and addressing stability and convergence issues.

Findings

Numerical results agree with theoretical predictions.

The formulation is stable and convergent under specified conditions.

Applicable to modeling interstitial fluid flow in brain tissue.

Abstract

A finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue. The formulation is based on the adoption of an ALE perspective. We focus on a flow regime in which inertia forces are negligible. The stability and convergence of the formulation is discussed, and numerical results demonstrate agreement with the theory.