Convergence of a finite volume scheme for the bidomain model of cardiac tissue

DOI10.1016/j.apnum.2008.12.016zbMath1165.92005OpenAlexW2050687996MaRDI QIDQ1030791

Mostafa Bendahmane, Kenneth Hvistendahl Karlsen

Publication date: 2 July 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.12.016

zbMATH Keywords

weak solutionfinite volume schemecardiac electric fielddegenerate reaction-diffusion system

Mathematics Subject Classification ID

Applications of functional analysis in biology and other sciences (46N60) Reaction-diffusion equations (35K57) Biophysics (92C05) Physiology (general) (92C30) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items

Uniform Null Controllability for a Degenerating Reaction-Diffusion System Approximating a Simplified Cardiac Model, A unified analysis for reaction-diffusion models with application to the spiral waves dynamics of the Barkley model, A positive cell vertex Godunov scheme for a Beeler–Reuter based model of cardiac electrical activity, Convergence analysis for virtual element discretizations of the cardiac bidomain model, Unnamed Item, Analysis of an optimal control problem for the tridomain model in cardiac electrophysiology, A NUMERICAL ANALYSIS OF A REACTION–DIFFUSION SYSTEM MODELING THE DYNAMICS OF GROWTH TUMORS, A finite volume scheme for cardiac propagation in media with isotropic conductivities, A multiresolution space-time adaptive scheme for the bidomain model in electrocardiology, Order optimal preconditioners for fully implicit Runge-Kutta schemes applied to the bidomain equations, Stability of conductivities in an inverse problem in the reaction-diffusion system in electrocardiology

Cites Work

• Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue
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• Discrete Sobolev inequalities andL^perror estimates for finite volume solutions of convection diffusion equations
• Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
• Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology
• Computing the Electrical Activity in the Heart
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