A posteriori error analysis for a coupled Stokes-poroelastic system with multiple compartments

TL;DR

This paper develops and verifies a posteriori error estimates for a complex coupled Stokes-MPE system modeling brain fluid dynamics, enabling adaptive mesh refinement to reduce computational costs.

Contribution

It introduces the first rigorous a posteriori error estimates for the coupled Stokes-MPE system in brain modeling, facilitating adaptive methods and reduced order modeling.

Findings

The a posteriori estimator is reliable and efficient.

Numerical experiments confirm the estimator's effectiveness.

Different solution variables influence the error estimates.

Abstract

The discretization of fluid-poromechanics systems is typically highly demanding in terms of computational effort. This is particularly true for models of multiphysics flows in the brain, due to the geometrical complexity of the cerebral anatomy - requiring a very fine computational mesh for finite element discretization - and to the high number of variables involved. Indeed, this kind of problems can be modeled by a coupled system encompassing the Stokes equations for the cerebrospinal fluid in the brain ventricles and Multiple-network Poro-Elasticity (MPE) equations describing the brain tissue, the interstitial fluid, and the blood vascular networks at different space scales. The present work aims to rigorously derive a posteriori error estimates for the coupled Stokes-MPE problem, as a first step towards the design of adaptive refinement strategies or reduced order models to decrease the computational demand of the problem. Through numerical experiments, we verify the reliability and optimal efficiency of the proposed a posteriori estimator and identify the role of the different solution variables in its composition.