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

Boris Andreianov (1) , Mostafa Bendahmane (2) , Kenneth Hvistendahl Karlsen (3) , Charles Pierre (4)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 IMB - Institut de Mathématiques de Bordeaux
3 CMA - Center of Mathematics for Applications [Oslo]
4 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

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.

Mots clés: Cardiac electrical activity; Bidomain model; Finite volume schemes; Convergence; Degenerate parabolic PDE

Domaines: Analyse numérique [math.NA]

Boris Andreianov, Mostafa Bendahmane, Kenneth Hvistendahl Karlsen, Charles Pierre. Convergence of discrete duality finite volume schemes for the cardiac bidomain model. Networks and Heterogeneous Media, 2011, In Press, pp.1-45. ⟨hal-00526047v2⟩