Optimal $L^2$-norm error estimate of multiphysics finite element method for poroelasticity model and simulating brain edema

TL;DR

This paper establishes an optimal $L^2$-norm error estimate for a multiphysics finite element method applied to poroelasticity, verifies it numerically, and uses it to simulate brain edema, analyzing key physical parameters' effects.

Contribution

It introduces an auxiliary problem to derive an optimal error estimate and applies the method to simulate brain edema, highlighting the influence of physical parameters.

Findings

Permeability $K$ significantly affects intracranial pressure and tissue deformation.

Young's modulus $E$ and Poisson ratio $ u$ mainly influence tissue deformation and edema development speed.

Numerical tests confirm the theoretical error estimate.

Abstract

In this paper, we derive an optimal $L^2$-norm error estimate of the multiphysics finite element method for the poroelasticity model by introducing an auxiliary problem. We show some numerical tests to verify the theoretical result and apply the multiphysics finite element method to simulate the brain edema which caused by abnormal accumulation of cerebrospinal fluid in injured areas. And we investigate the effects of the key physical parameters on brain edema and observed that the permeability $K$ has the biggest influence on intracranial pressure and tissue deformation, Young's modulus $E$ and Poisson ratio $\nu$ have little effect on the maximum value of intracranial pressure, but have great effect on the tissue deformation and the developing speed of brain edema.