We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of the heart. We derive a posteriori error estimators accounting for different sources of error (space/time discretization and linearization). We prove reliability and efficiency (this latter under a suitable assumption) of the error indicators. Finally, numerical experiments assess the validity of the theoretical results.

A posteriori error estimates for the monodomain model in cardiac electrophysiology

Verani M.
2019-01-01

Abstract

We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of the heart. We derive a posteriori error estimators accounting for different sources of error (space/time discretization and linearization). We prove reliability and efficiency (this latter under a suitable assumption) of the error indicators. Finally, numerical experiments assess the validity of the theoretical results.
2019
A posteriori error estimates; Adaptive Newton–Galerkin method; Cardiac electrophysiology; Nonlinear initial-boundary value problem
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1109086
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