J. T. Beale and A. T. Layton, On the accuracy of finite difference methods for elliptic problems with interfaces, Communications in Applied Mathematics and Computational Science, vol.37, issue.1, pp.91-119, 2006.
DOI : 10.1016/S1570-8659(05)80039-0

P. Bethelsen, A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions, Journal of Computational Physics, vol.197, issue.1, pp.364-386, 2004.
DOI : 10.1016/j.jcp.2003.12.003

D. Bresch, T. Colin, E. Grenier, B. Ribba, and O. Saut, Computational Modeling of Solid Tumor Growth: The Avascular Stage, SIAM Journal on Scientific Computing, vol.32, issue.4, pp.2321-2344, 2009.
DOI : 10.1137/070708895

URL : https://hal.archives-ouvertes.fr/inria-00148610

F. Buret, N. Faure, L. Nicolas, R. Perussel, and C. Poignard, Numerical studies on the effect of electric pulses on an egg-shaped cell with a spherical nucleus, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00477495

I. Chern and Y. Shu, A coupling interface method for elliptic interface problems, Journal of Computational Physics, vol.225, issue.2, pp.2138-2174, 2007.
DOI : 10.1016/j.jcp.2007.03.012

URL : http://ntur.lib.ntu.edu.tw/news/agent_contract.pdf

P. G. Ciarlet, Discrete maximum principle for finite-difference operators. aequationes mathematicae, pp.338-352, 1970.
DOI : 10.1007/bf01844166

M. Cisternino and L. Weynans, Abstract, Communications in Computational Physics, vol.39, issue.05, pp.1562-1587, 2012.
DOI : 10.1016/j.jcp.2006.02.014

F. Gibou, R. P. Fedkiw, L. T. Cheng, and M. Kang, A Second-Order-Accurate Symmetric Discretization of the Poisson Equation on Irregular Domains, Journal of Computational Physics, vol.176, issue.1, pp.205-227, 2002.
DOI : 10.1006/jcph.2001.6977

F. Gibou and R. P. Fedkiw, A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem, Journal of Computational Physics, vol.202, issue.2, pp.577-601, 2005.
DOI : 10.1016/j.jcp.2004.07.018

A. Guittet, M. Lepilliez, S. Tanguy, and F. Gibou, Solving elliptic problems with discontinuities on irregular domains ??? the Voronoi Interface Method, Journal of Computational Physics, vol.298, pp.747-765, 2015.
DOI : 10.1016/j.jcp.2015.06.026

H. Huang and Z. Li, Convergence analysis of the immersed interface method, IMA Journal of Numerical Analysis, vol.19, issue.4, pp.583-608, 1999.
DOI : 10.1093/imanum/19.4.583

O. Kavian, M. Leguebe, C. Poignard, and L. Weynans, ???Classical??? Electropermeabilization Modeling at the Cell Scale, Journal of Mathematical Biology, vol.1724, issue.4, pp.235-265, 2014.
DOI : 10.1016/j.bbagen.2005.05.006

URL : https://hal.inria.fr/hal-00712683/document

M. Leguebe, C. Poignard, and L. Weynans, A second-order Cartesian method for the simulation of electropermeabilization cell models, Journal of Computational Physics, vol.292, pp.114-140, 2015.
DOI : 10.1016/j.jcp.2015.03.028

URL : https://hal.archives-ouvertes.fr/hal-01158377

R. J. Leveque and L. Z. Li, The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources, SIAM Journal on Numerical Analysis, vol.31, issue.4, pp.1019-1044, 1994.
DOI : 10.1137/0731054

Z. L. Li, A Fast Iterative Algorithm for Elliptic Interface Problems, SIAM Journal on Numerical Analysis, vol.35, issue.1, pp.230-254, 1998.
DOI : 10.1137/S0036142995291329

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.4686

Z. L. Li and K. Ito, Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients, SIAM Journal on Scientific Computing, vol.23, issue.1, pp.339-361, 2001.
DOI : 10.1137/S1064827500370160

X. Liu, R. Fedkiw, and M. Kang, A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains, Journal of Computational Physics, vol.160, issue.1, pp.151-178, 2000.
DOI : 10.1006/jcph.2000.6444

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.5776

M. Bergmann and L. Weynans, A sharp cartesian method for incompressible flows with large density ratios
URL : https://hal.archives-ouvertes.fr/hal-01331234

A. Mayo, The Fast Solution of Poisson???s and the Biharmonic Equations on Irregular Regions, SIAM Journal on Numerical Analysis, vol.21, issue.2, pp.285-299, 1984.
DOI : 10.1137/0721021

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, 2003.
DOI : 10.1115/1.1760520

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, p.79, 1988.
DOI : 10.1016/0021-9991(88)90002-2

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.5254

J. A. Sethian, Level Set Methods and Fast Marching Methods, 1999.

J. A. Sethian, Evolution, Implementation, and Application of Level Set and Fast Marching Methods for Advancing Fronts, Journal of Computational Physics, vol.169, issue.2, pp.503-555, 2001.
DOI : 10.1006/jcph.2000.6657

A. Wiegmann and K. Bube, The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions, SIAM Journal on Numerical Analysis, vol.37, issue.3, pp.827-862, 2000.
DOI : 10.1137/S0036142997328664

S. Yu and G. W. Wei, Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities, Journal of Computational Physics, vol.227, issue.1, pp.602-632, 2007.
DOI : 10.1016/j.jcp.2007.08.003