A posteriori error estimates for the monodomain model in cardiac\n electrophysiology

2019/01/22 by Luca Ratti, Ratti, Luca, Marco Verani +1
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1901.07468

openalex publication_date 2019/01/22 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

We consider the monodomain model, a system of a parabolic semilinear\nreaction-diffusion equation coupled with a nonlinear ordinary differential\nequation, arising from the (simplified) mathematical description of the\nelectrical activity of the heart. We derive a posteriori error estimators\naccounting for different sources of error (space/time discretization and\nlinearization). We prove reliability and efficiency (this latter under a\nsuitable assumption) of the error indicators. Finally, numerical experiments\nassess the validity of the theoretical results.\n

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