Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology
Simona Sanfelici · Numerical Methods for Partial Differential Equations · 2002
Abstract In this work we consider the reaction‐diffusion system of FitzHugh‐Nagumo type describing the behavior of the electrical conduction in an anisotropic cardiac muscle. 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. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 218–240, 2002; DOI 10.1002/num.1000