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Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2006

Stability and convergence of a finite volume method for two systems of reaction-diffusion equations in electro-cardiology

Yves Coudière
Charles Pierre

Résumé

The monodomain equations model the propagation of the action potential in the human heart: a very sharp pulse propagating at a high speed, which computation require fine unstructured 3D meshes. It is a non linear parabolic PDE of reaction diffusion type, coupled to one or several ODE, with multiple time-scales. Numerical difficulties, such as unstructured meshes and stability are addressed here through the use of a finite volume method. Stability conditions are given for two time-stepping methods, and two example sets of ODEs, convergence is proved and error estimates are computed.
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Dates et versions

hal-00016816 , version 1 (11-01-2006)

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Yves Coudière, Charles Pierre. Stability and convergence of a finite volume method for two systems of reaction-diffusion equations in electro-cardiology. Nonlinear Analysis: Theory, Methods and Applications, 2006, 7, pp.Pages 916-935. ⟨10.1016/j.nonrwa.2005.02.006⟩. ⟨hal-00016816⟩
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