PUMA
Istituto di Matematica Applicata e Tecnologie Informatiche     
Sanfelici S. Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology. Technical report ercim.cnr.ian//1998-1120, 1998.
 
 
Abstract
(English)
In this work we consider the reaction-diffusion system of FitzHugh-Nagumo type describing the behaviour of the electrical conduction in anisotropic cardiac muscle. The coupling between the intra and extracellular media gives rise to a reaction-diffusion system of degenerate parabolic type, therefore the analysis of the Galerkin semidiscrete space approximation to this system is approached by means of a suitable variational formulation in the framework of abstract degenerate evolution equations. The main results concern convergence analysis and a priori stability estimates for the semidiscrete solution. These abstract results are then applied to the cardiac problem and for the finite element Galerkin approximation we achieve optimal order convergence.
Subject Degenerate evolution system, Galerkin approximation



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