Convergence of discrete duality finite volume schemes for the cardiac bidomain model

TL;DR

This paper proves the convergence of discrete duality finite volume schemes on distorted meshes for simplified cardiac bidomain models, including numerical tests validating the theoretical results.

Contribution

It establishes convergence results for DDFV schemes applied to cardiac bidomain models on complex meshes, extending previous work to more realistic geometries.

Findings

Convergence of DDFV schemes on distorted meshes.

Validation through numerical tests.

Applicability to 3D cardiac models.

Abstract

We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes are treated. A short description is given of the 3D DDFV meshes and of some of the associated discrete calculus tools. Several numerical tests are presented.