Speaker
Description
Multiple sclerosis is a complex neurodegenerative disorder whose progression can be described through nonlinear mathematical models accounting for both inflammatory and degenerative processes.
In this work, we investigate the application of the Hybridized Discontinuous Galerkin (HDG) method to the numerical approximation of such models.
The HDG framework retains the flexibility of discontinuous Galerkin schemes while significantly reducing the number of globally coupled degrees of freedom, thereby enhancing computational efficiency without sacrificing accuracy.
We consider the model introduced in \cite{desvillettes2022global}, derive the corresponding HDG discretization, and provide a rigorous convergence analysis of the proposed method.
The theoretical findings are validated by numerical experiments confirming the predicted convergence behavior. Overall, the results highlight the suitability of HDG methods for the simulation of multiple sclerosis dynamics and support their use as reliable tools for the numerical approximation of complex biomedical models.
This work is realized with the support of the Italian Ministry of Research, under the complementary action NRRP “D34Health - Digital Driven Diagnostics, prognostics and therapeutics for sustainable Health care” (Grant #PNC0000001).
Bibliography
@article{desvillettes2022global,
title={Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis},
author={Desvillettes, Laurent and Giunta, Valeria and Morgan, Jeff and Tang, Bao Quoc},
journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
volume={152},
number={4},
pages={826--856},
year={2022},
publisher={Cambridge University Press},
doi={10.1017/prm.2021.33}
}
