I. Babu?ka, U. Banerjee, and J. E. Osborn, Superconvergence in the generalized finite element method, Numerische Mathematik, vol.71, issue.221, pp.353-395, 2007.
DOI : 10.1007/s00211-007-0096-8

H. Chen, C. Min, and F. Gibou, A Supra-Convergent Finite Difference Scheme for the Poisson and Heat Equations on Irregular Domains and Non-Graded Adaptive Cartesian Grids, Journal of Scientific Computing, vol.92, issue.1, pp.19-60, 2007.
DOI : 10.1007/s10915-006-9122-8

P. G. Ciarlet, Discrete maximum principle for finite-difference operators. aequationes mathematicae, pp.338-352, 1970.

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

R. P. Fedkiw, T. Aslam, B. Merriman, and S. Osher, A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method), Journal of Computational Physics, vol.152, issue.2, pp.457-492, 1999.
DOI : 10.1006/jcph.1999.6236

A. José, R. D. Ferreira, and . Grigorieff, On the supraconvergence of elliptic finite difference schemes, Applied Numerical Mathematics, vol.28, pp.2-4275, 1998.

O. Gallinato, M. Ohta, C. Poignard, and T. Suzuki, Free boundary problem for cell protrusion formations: theoretical and numerical aspects, Journal of Mathematical Biology, vol.18, issue.1, pp.35-01228013, 2015.
DOI : 10.1007/s00285-016-1080-7
URL : https://hal.archives-ouvertes.fr/hal-01412264

F. Gibou, R. P. Fedkiw, L. 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

N. Levine, Superconvergent Recovery of the Gradient from Piecewise Linear Finite-element Approximations, IMA Journal of Numerical Analysis, vol.5, issue.4, pp.407-427, 1985.
DOI : 10.1093/imanum/5.4.407

Z. Li, T. Yamamoto, and Q. Fang, Superconvergence of solution derivatives for the Shortley???Weller difference approximation of Poisson's equation. Part I: smoothness problems, Journal of Computational and Applied Mathematics, vol.151, issue.2, pp.307-333, 2003.
DOI : 10.1016/S0377-0427(02)00754-9

N. Matsunaga and T. Yamamoto, Superconvergence of the Shortley???Weller approximation for Dirichlet problems, Journal of Computational and Applied Mathematics, vol.116, issue.2, pp.263-273, 2000.
DOI : 10.1016/S0377-0427(99)00321-0

C. Min, F. Gibou, and H. D. Ceniceros, A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids, Journal of Computational Physics, vol.218, issue.1, pp.123-140, 2006.
DOI : 10.1016/j.jcp.2006.01.046

H. George, R. Shortley, and . Weller, The Numerical Solution of Laplace's Equation, Journal of Applied Physics, vol.9, issue.5, p.334, 1938.

L. Weynans, A proof in the finite-difference spirit of the superconvergence of the gradient for the Shortley-Weller method, Research Report, pp.14-01176994

G. Yoon and C. Min, Convergence Analysis of the Standard Central Finite Difference Method for Poisson Equation, Journal of Scientific Computing, vol.18, issue.2, pp.1-16, 2015.
DOI : 10.1007/s10915-015-0096-2

M. Zlámal, Superconvergence and Reduced Integration in the Finite Element Method, Mathematics of Computation, vol.32, issue.143, pp.663-685, 1978.
DOI : 10.2307/2006479