# A posteriori error estimates for the monodomain model in cardiac electrophysiology

## TL;DR

This paper develops and validates a posteriori error estimators for the monodomain model in cardiac electrophysiology, enabling accurate assessment of numerical solution errors from discretization and linearization.

## Contribution

It introduces reliable and efficient a posteriori error estimators for the monodomain model, accounting for multiple error sources and supported by numerical validation.

## Key findings

- Error estimators are reliable and efficient under certain conditions.
- Numerical experiments confirm the theoretical error bounds.
- The approach improves error control in cardiac electrophysiology simulations.

## 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.