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

Abstract : 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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Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2006, 7, pp.Pages 916-935. 〈10.1016/j.nonrwa.2005.02.006〉
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https://hal.archives-ouvertes.fr/hal-00016816
Contributeur : Yves Coudière <>
Soumis le : mercredi 11 janvier 2006 - 14:30:20
Dernière modification le : lundi 25 mars 2019 - 16:52:05
Document(s) archivé(s) le : samedi 3 avril 2010 - 21:09:56

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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, Elsevier, 2006, 7, pp.Pages 916-935. 〈10.1016/j.nonrwa.2005.02.006〉. 〈hal-00016816〉

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