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

Applied Numerical Mathematics

Volumn 59, Issue 9, 2009, Pages 2266-2284

  Bendahmane, Mostafa ^a   Karlsen, Kenneth H ^b,c  

^a UNIVERSITY OF CONCEPCIÓN   (Chile)

^b UNIVERSITY OF OSLO   (Norway)

^c SIMULA RESEARCH LABORATORY   (Norway)

Author keywords

Cardiac electric field; Degenerate reaction diffusion system; Finite volume scheme; Weak solution

Indexed keywords

A-PRIORI ESTIMATES; BIDOMAIN MODELS; CARDIAC ELECTRIC FIELD; CARDIAC TISSUES; COMPACTNESS CRITERION; DEGENERATE REACTION-DIFFUSION SYSTEM; EXISTENCE AND UNIQUENESS OF SOLUTION; FINITE VOLUME SCHEME; FINITE VOLUME SCHEMES; WEAK SOLUTION;

ELECTRIC FIELDS; NONLINEAR EQUATIONS;

DIFFUSION IN LIQUIDS;

EID: 67349199962     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2008.12.016     Document Type: Article

References (18)

1. Ambrosio L., Colli Franzone P., and Savaré G. On the asymptotic behaviour of anisotropic energies arising in the cardiac bidomain model. Interfaces Free Bound. 2 3 (2000) 213-266
2. Bendahmane M., and Karlsen K.H. Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue. Networks and Heterogeneous Media 1 1 (2006) 185-218
3. Brezis H. Analyse fonctionnelle, Théorie et Applications (1983), Masson, Paris
4. Chainais-Hillairet C., Liu J.-G., and Peng Y.-J. Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. M2AN Math. Model. Numer. Anal. 37 2 (2003) 319-338
5. Colli Franzone P., and Savaré G. Degenerate evolution systems modeling the cardiac electric field at micro- and macroscopic level. Evolution Equations, Semigroups and Functional Analysis. Milan, 2000. Progr. Nonlinear Differential Equations Appl. vol. 50 (2002), Birkhäuser, Basel 49-78
6. p error estimates for finite volume solutions of convection diffusion equations. M2AN Math. Model. Numer. Anal. 35 4 (2001) 767-778
7. Eymard R., Gallouët T., Herbin R., and Michel A. Convergence of a finite volume scheme for nonlinear degenerate parabolic equations. Numer. Math. 92 1 (2002) 41-82
8. Eymard R., Gallouët Th., and Herbin R. Finite volume methods. Handbook of Numerical Analysis vol. VII (2000), North-Holland, Amsterdam
9. Fairweather G. Finite Element Galerkin Methods for Differential Equations. Lecture Notes in Pure and Applied Mathematics vol. 34 (1978), Marcel Dekker, Inc., New York-Basel
10. Henrique C.S. Simulating the electrical behavior of cardiac tissue using the bidomain models. Crit. Rev. Biomed. Eng. 21 (1993) 1-93
11. Herbin R. Finite volume methods for diffusion convection equations on general meshes. In: Benkhaldoun F., and Vilsmeier R. (Eds). Finite Volumes for Complex Applications, Problems and Perspectives (1996), Hermes, Paris 153-160
12. Keener J., and Sneyd J. Mathematical Physiology (1998), Springer-Verlag, New York
13. Lions J.-L. Quelques méthodes de résolution des problèmes aux limites non linéaires (1969), Dunod, Paris
14. Sachse F.B. Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics. Lecture Notes in Comput. Sci. vol. 2966 (2004), Springer, Berlin
15. Sanfelici S. Numerical and analytic study of a parabolic-ordinary system modelling cardiac activation under equal anisotropy conditions. Riv. Mat. Univ. Parma 5 5 (1996) 143-157
16. Sanfelici S. Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology. Numer. Methods Partial Differential Equations 18 2 (2002) 218-240
17. Sundnes J., Lines G.T., Cai X., Nielsen B.F., Mardal K.-A., and Tveito A. Computing the Electrical Activity in the Heart. Monographs in Computational Science and Engineering vol. 1 (2006), Springer-Verlag, Berlin
18. Temam R. Navier-Stokes Equations, Theory and Numerical Analysis. 3rd revised edition (2001), North-Holland, Amsterdam reprinted in the AMS Chelsea series, Amer. Math. Soc., Providence, RI