Advanced Finite Element Methods in Brain Fluid Simulations with Applications to the Clearance During Sleep

• Grant number: 25/09660-0
• Support Opportunities: Scholarships abroad - Research
• Start date: August 18, 2025
• End date: December 17, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Sônia Maria Gomes
• Grantee: Sônia Maria Gomes
• Host Investigator: Kent-Andre Mardal
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Company: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Mecânica (FEM)
• Institution abroad: Simula Research Laboratory, Norway
• Associated research grant: 17/15736-3 - Engineering Research Centre in Reservoir and Production Management, AP.PCPE

Abstract

The main objective of the project is to facilitate a first-step in building of a promising collaboration with a research group in the Simula Research Laboratory, University of Oslo, Norway, on advanced computational modeling using finite element methods. Specially, the main application interest is in the understanding of brain fluid dynamics, which can be seen as a multiphysics Biot-Stokes type problem. Discarding elasticity effects in this early collaboration stage, numerical approximations of fluid velocity and pressure in Stokes and Darcy regimes shall be considered by a semi-hybrid-mixed finite element method based on divergence-compatible finite elements pairs in H(div) × L2. This way, continuous normal traces in all element interfaces are taken for granted, and using hybridization, the interface tangential velocity continuity, required for Stokes flows, is weakly enforced by an additional Lagrange multiplier variable. Advancing toward the ultimate objective of mastering robust computational simulation models for brain clearance, the main goals to be pursued during the visit are: improvement of stability and error analyses of the semi-hybrid-mixed methods for Stokes and Stokes-Darcy sub-problems; investigation of efficient iterative solvers for the global systems occurring in the static condensation procedure; and comparison of the method results to previous standard schemes in terms of efficiency, accuracy and robustness with respect to material parameter variations and sensitivity to model geometry.