AuthorsE. Ødegaard
EditorsM. E. Rognes
TitleA posteriori error estimation for multiple-network poroelasticity
AfilliationScientific Computing
Project(s)Waterscape: The Numerical Waterscape of the Brain
Publication TypeMaster's thesis
Year of Publication2018
Degree awarding institutionThe University of Oslo
Date Published08/2018
PublisherThe University of Oslo
Place PublishedOslo, Norway
Keywordsa posteriori error estimates, generalized poroelasticity, MPET

The multiple network poroelasticity equations (MPET) describe mechanical deformation and fluid flow in porous media and can be used to understand various biological processes in a physiological setting.  Modeling transportation of fluid within the brain is essential to discover the underlying mechanisms that are currently being investigated concerning various neurodegenerative diseases such as Alzheimer's disease.  Mathematical modeling is considered to be more accessible and less expensive than performing advanced medical tests and experiments; however, numerical simulations are still prone to error, making it essential to control and minimize.  Physiological frameworks often include complex geometries which may produce complex error distributions.  A posterior error estimation presents a framework to measure and control the error in specific regions of the computational domain.  This thesis presents the derivation of a posteriori error estimates for MPET with two interacting fluid networks, extending the analysis from on fluid network.  The presented estimates can be extended to the MPET model with an arbitrary number of networks, which is demonstrated with a computational experiment using four networks on a brain mesh with physiologically inspired parameters.

Citation Key26142