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Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology
Author(s) -
Sanfelici Simona
Publication year - 2002
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1000
Subject(s) - galerkin method , mathematics , degenerate energy levels , convergence (economics) , finite element method , a priori and a posteriori , stability (learning theory) , partial differential equation , mathematical analysis , space (punctuation) , work (physics) , computer science , physics , philosophy , epistemology , quantum mechanics , machine learning , economics , thermodynamics , economic growth , operating system
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