Hybridized Discontinuous Galerkin Discretization for a Mathematical Model of Multiple Sclerosis
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Multiple sclerosis is a complex neurodegenerative disease whose evolution can be described by nonlinear mathematical models capturing both inflammatory and degenerative mechanisms. In this work we apply the Hybridized Discontinuous Galerkin (HDG) method to mathematical models of multiple sclerosis. The HDG approach combines the flexibility of discontinuous Galerkin discretizations with a reduced number of globally coupled degrees of freedom, resulting in efficient and accurate numerical schemes. We focus on the model studied in [2], present the corresponding HDG formulation, and establish theoretical convergence results for the proposed discretization. The theoretical analysis is supported by numerical experiments based on the model proposed in [3], confirming the expected convergence rates. These results demonstrate the effectiveness of the HDG method for simulating multiple sclerosis dynamics and highlight its potential for reliable numerical approximation of complex biomedical systems. 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).
