Convergence of discrete duality finite volume schemes for the cardiac bidomain model
Provides theoretical convergence guarantees for numerical simulations of cardiac electrical activity, relevant for computational cardiology.
The paper proves convergence of discrete duality finite volume schemes for simplified cardiac bidomain models on distorted meshes, covering both time-implicit and linearised schemes, with numerical tests confirming the results.
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.