E. Allen, S. Novosel, and Z. Zhang, Finite element and difference approximation of some linear stochastic partial differential equations, Stochastics An International Journal of Probability and Stochastic Processes, vol.64, issue.1, pp.117-142, 1998.
DOI : 10.1080/17442509808834159

I. Babuska, B. Szabo, and I. Katz, -Version of the Finite Element Method, SIAM Journal on Numerical Analysis, vol.18, issue.3, pp.515-545, 1981.
DOI : 10.1137/0718033
URL : https://hal.archives-ouvertes.fr/hal-00531872

D. Barkley, A model for fast computer simulation of waves in excitable media, Physica D: Nonlinear Phenomena, vol.49, issue.1-2, pp.61-70, 1991.
DOI : 10.1016/0167-2789(91)90194-E

D. Barkley, Linear stability analysis of rotating spiral waves in excitable media, Physical Review Letters, vol.68, issue.13, pp.2090-2093, 1992.
DOI : 10.1103/PhysRevLett.68.2090

D. Barkley, Euclidean symmetry and the dynamics of rotating spiral waves, Physical Review Letters, vol.72, issue.1, pp.164-167, 1994.
DOI : 10.1103/PhysRevLett.72.164

D. Barkley, M. Kness, and L. Tuckerman, Spiral-wave dynamics in a simple model of excitable media: The transition from simple to compound rotation, Physical Review A, vol.42, issue.4, pp.2489-2492, 1990.
DOI : 10.1103/PhysRevA.42.2489

N. Berglund and B. Gentz, Noise-induced phenomena in slow-fast dynamical systems: a sample-paths approach, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00010168

S. Bonaccorsi and E. Mastrogiacomo, ANALYSIS OF THE STOCHASTIC FITZHUGH???NAGUMO SYSTEM, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol.11, issue.03, pp.427-446, 2008.
DOI : 10.1142/S0219025708003191

M. Boulakia, S. Cazeau, M. Fernández, J. F. Gerbeau, and N. Zemzemi, Mathematical Modeling of Electrocardiograms: A Numerical Study, Annals of Biomedical Engineering, vol.98, issue.1???3, pp.1071-1097, 2010.
DOI : 10.1007/s10439-009-9873-0
URL : https://hal.archives-ouvertes.fr/inria-00400490

C. E. Bréhier, Strong and weak orders in averaging for SPDEs, Stochastic Processes and their Applications, vol.122, issue.7, pp.2553-2593, 2012.
DOI : 10.1016/j.spa.2012.04.007

Y. Cao, H. Yang, and H. Yin, Finite element methods for semilinear elliptic stochastic partial differential equations, Numerische Mathematik, vol.187, issue.4, pp.181-198, 2007.
DOI : 10.1007/s00211-007-0062-5

S. Cerrai and M. Freidlin, Averaging principle for a class of stochastic reaction???diffusion equations, Probability Theory and Related Fields, vol.17, issue.1-2, pp.137-177, 2009.
DOI : 10.1007/s00440-008-0144-z

P. Ciarlet and J. Lions, Finite Element Methods, Handbook of Numerical Analysis, 1991.

D. Prato and G. , Kolmogorov Equations for Stochastic PDEs, Birkhäuser Basel, 2004.
DOI : 10.1007/978-3-0348-7909-5

D. Prato, G. Zabczyk, and J. , Stochastic equations in infinite dimensions, 1992.

A. Debussche and J. Printems, Weak order for the discretization of the stochastic heat equation, Mathematics of Computation, vol.78, issue.266, pp.845-863, 2009.
DOI : 10.1090/S0025-5718-08-02184-4
URL : https://hal.archives-ouvertes.fr/hal-00183249

R. Fitzhugh, Mathematical models of excitation and propagation in nerve, Biological Engineering, 1969.

L. Goudenège, D. Martin, and G. Vial, High Order Finite Element Calculations for the Cahn-Hilliard Equation, Journal of Scientific Computing, vol.227, issue.1, pp.294-321, 2012.
DOI : 10.1007/s10915-011-9546-7

M. Hairer, M. Ryser, and H. Weber, Triviality of the 2D stochastic Allen-Cahn equation, Electronic Journal of Probability, vol.17, issue.0, pp.1-14, 2012.
DOI : 10.1214/EJP.v17-1731

F. Hecht, L. Hyaric, A. Ohtsuka, K. Pironneau, O. Hinch et al., Freefem++, finite elements software 21 An analytical study of the physiology and pathology of the propagation of cardiac action potentials, Progress in Biophys. and Mol. Bio, vol.78, issue.1, pp.45-81, 2002.

A. Hodgkin and A. Huxley, Propagation of Electrical Signals Along Giant Nerve Fibres, Proceedings of the Royal Society B: Biological Sciences, vol.140, issue.899, pp.177-183, 1952.
DOI : 10.1098/rspb.1952.0054

A. Jentzen, Pathwise numerical approximations of SPDEs with additive noise under non-global lipschitz coefficients. Potential Anal, pp.375-404, 2009.

A. Jentzen and M. Röckner, A Milstein scheme for SPDEs. arXiv preprint arXiv:1001, p.2751, 2012.

P. Jordan and D. Christini, Cardiac Arrhythmia, 2006.
DOI : 10.1002/9780471740360.ebs0217

J. Keener, Waves in Excitable Media, SIAM Journal on Applied Mathematics, vol.39, issue.3, pp.528-548, 1980.
DOI : 10.1137/0139043

M. Kovács, S. Larsson, and F. Lindgren, Strong convergence of the finite element method with truncated noise for semilinear parabolic stochastic equations with additive noise, Numerical Algorithms, vol.43, issue.2-3, pp.309-320, 2010.
DOI : 10.1007/s11075-009-9281-4

R. Kruse, Optimal error estimates of Galerkin finite element methods for stochastic partial differential equations with multiplicative noise, IMA Journal of Numerical Analysis, vol.34, issue.1, pp.217-251, 2014.
DOI : 10.1093/imanum/drs055

R. Kruse and S. Larsson, Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise, Electronic Journal of Probability, vol.17, issue.0, pp.1-19, 2012.
DOI : 10.1214/EJP.v17-2240

B. Lindner, J. Garcia-ojalvo, A. Neiman, and L. Schimansky-geier, Effects of noise in excitable systems, Physics Reports, vol.392, issue.6, pp.321-424, 2004.
DOI : 10.1016/j.physrep.2003.10.015

G. Lord and A. Tambue, A modified semi-implict Euler-Maruyama scheme for finite element discretization of SPDEs. arXiv preprint arXiv:1004, 1998.

G. Lord and A. Tambue, Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise, IMA Journal of Numerical Analysis, vol.33, issue.2, pp.515-543, 2013.
DOI : 10.1093/imanum/drr059

G. Lord and V. Thümmler, Computing Stochastic Traveling Waves, SIAM Journal on Scientific Computing, vol.34, issue.1, pp.24-43, 2012.
DOI : 10.1137/100784734

C. Mitchell and D. Schaeffer, A two-current model for the dynamics of cardiac membrane, Bulletin of Mathematical Biology, vol.65, issue.5, pp.767-793, 2003.
DOI : 10.1016/S0092-8240(03)00041-7

S. Peszat and J. Zabczyk, Stochastic Partial Differential Equations with Lévy Noise, 2007.
DOI : 10.1017/CBO9780511721373

P. Raviart and J. Thomas, Introduction à l'analyse numérique des équations aux dérivées partielles, 1983.

T. Shardlow, Numerical simulation of stochastic PDEs for excitable media, Journal of Computational and Applied Mathematics, vol.175, issue.2, pp.429-446, 2005.
DOI : 10.1016/j.cam.2004.06.020

H. Tuckwell and J. Jost, Weak Noise in Neurons May Powerfully Inhibit the Generation of Repetitive Spiking but Not Its Propagation, PLoS Computational Biology, vol.38, issue.5, 2010.
DOI : 10.1371/journal.pcbi.1000794.g011

D. Wagner, Survey of measurable selection theorems: An update, Lecture Notes in Mathematics, vol.59, 1980.
DOI : 10.2140/pjm.1975.59.267

J. Walsh, Finite element methods for parabolic stochastic PDEs. Potential Anal, pp.1-43, 2005.

W. Wang and A. Roberts, Average and deviation for slow???fast stochastic partial differential equations, Journal of Differential Equations, vol.253, issue.5, pp.1265-1286, 2012.
DOI : 10.1016/j.jde.2012.05.011

Y. Yan, Galerkin Finite Element Methods for Stochastic Parabolic Partial Differential Equations, SIAM Journal on Numerical Analysis, vol.43, issue.4, pp.1363-1384, 2005.
DOI : 10.1137/040605278