L. Alvarez, F. Guichard, P. Lions, and J. Morel, Axioms and fundamental equations of image processing, Archive for Rational Mechanics and Analysis, vol.11, issue.3, pp.199-257, 1993.
DOI : 10.1117/12.7974127

L. Alvarez and J. Morel, Formalization and computational aspects of image analysis, Acta Numerica, vol.1, pp.200-257, 1993.
DOI : 10.1137/0729052

B. Andrews, Evolving convex curves, Calculus of Variations and Partial Differential Equations, vol.7, issue.4, pp.315-371, 1998.
DOI : 10.1007/s005260050111

B. Andrews, Classification of limiting shapes for isotropic curve flows, Journal of the American Mathematical Society, vol.16, issue.02, pp.443-459, 2003.
DOI : 10.1090/S0894-0347-02-00415-0

S. B. Angement, G. Sapiro, and A. Tannenbaum, On affine heat equation for non-convex curves, Journal of the American Mathematical Society, vol.11, issue.03, pp.601-634, 1998.
DOI : 10.1090/S0894-0347-98-00262-8

J. W. Barrett, H. Garcke, and R. Nürnberg, On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations, SIAM Journal on Scientific Computing, vol.29, issue.3, pp.1006-1041, 2007.
DOI : 10.1137/060653974

J. W. Barrett, H. Garcke, and R. Nürnberg, On the parametric finite element approximation of evolving hypersurfaces in <mml:math altimg="si82.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>, Journal of Computational Physics, vol.227, issue.9, pp.4281-4307, 2008.
DOI : 10.1016/j.jcp.2007.11.023

J. W. Barrett, H. Garcke, and R. Nürnberg, Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves, Numerische Mathematik, vol.34, issue.4, pp.489-542, 2012.
DOI : 10.1166/jctn.2008.2485

P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn et al., A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE, Computing, vol.24, issue.1, pp.121-138, 2008.
DOI : 10.1007/978-3-642-57172-5_2

P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn et al., A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework, Computing, vol.82, issue.2-3, pp.103-119, 2008.
DOI : 10.1007/s00607-008-0003-x

P. Bastian, F. Heimann, and S. Marnach, Generic implementation of finite element methods in the distributed and unified numerics environment (dune), Kybernetika, vol.46, issue.2, pp.294-315, 2010.

G. Bellettini and I. Fragalá, Elliptic approximations pf prescribed mean curvature surfaces in Finsler geometry, Asymptotic Anal, vol.22, issue.2, pp.87-111, 2000.

M. Blatt and P. Bastian, The Iterative Solver Template Library, 2007.
DOI : 10.1007/978-3-540-75755-9_82

URL : http://www.dune-project.org/publications/istl_para06.pdf

J. W. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, Texts in Applied Mathematics, vol.15, 1996.

E. Carlini, M. Falcone, and F. , Convergence of a large time-step scheme for mean curvature motion, Interfaces and Free Boundaries, vol.12, pp.409-441, 2010.
DOI : 10.4171/IFB/240

V. Caselles, F. Catte, T. Coll, and F. Dibos, A geometric model for active contours in image processing, Numerische Mathematik, vol.36, issue.4, pp.1-31, 1993.
DOI : 10.1007/BF01385685

T. Chan and L. Vese, An Active Contour Model without Edges, Scale-Space'99, pp.141-151, 1999.
DOI : 10.1007/3-540-48236-9_13

URL : http://www.math.ucla.edu/~lvese/PAPERS/SS99.pdf

Y. G. Chen, Y. Giga, and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, Proc. Japan. Acad, pp.207-210, 1989.

Y. G. Chen, Y. Giga, and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, Journal of Differential Geometry, vol.33, issue.3, pp.749-786, 1991.
DOI : 10.4310/jdg/1214446564

M. G. Crandall, H. Ishii, and P. Lions, user's guide to viscosity solutions\\ of second order\\ partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

M. G. Crandall and P. Lions, Convergent difference schemes for nonlinear parabolic equations and mean curvature motion, Numerische Mathematik, vol.75, issue.1, pp.17-41, 1996.
DOI : 10.1007/s002110050228

K. Deckelnick, Error bounds for a difference scheme approximating viscosity solutions of mean curvature flow. Interfaces Free Bound, pp.117-142, 2000.

K. Deckelnick and G. Dziuk, Convergence of a finite element method for non-parametric mean curvature flow, Numerische Mathematik, vol.72, issue.2, pp.197-222, 1995.
DOI : 10.1007/s002110050166

K. Deckelnick, G. Dziuk, and C. M. Elliott, Computation of geometric partial differential equations and mean curvature flow, Acta Numerica, vol.14, pp.139-232, 2005.
DOI : 10.1017/S0962492904000224

K. Deckelnick and G. Dziuk, CONVERGENCE OF NUMERICAL SCHEMES FOR THE APPROXIMATION OF LEVEL SET SOLUTIONS TO MEAN CURVATURE FLOW, Series Adv. Math. Appl. Sciences, vol.59, pp.77-94, 2001.
DOI : 10.1142/9789812799807_0005

K. Ecker and G. Huisken, Mean Curvature Evolution of Entire Graphs, The Annals of Mathematics, vol.130, issue.3, pp.453-471, 1989.
DOI : 10.2307/1971452

L. C. Evans and J. Spruck, Motion of level sets by mean curvature. I, Journal of Differential Geometry, vol.33, issue.3, pp.635-681, 1991.
DOI : 10.4310/jdg/1214446559

X. Feng, M. Neilan, and A. Prohl, Error analysis of finite element approximations of the inverse mean curvature flow arising from the general relativity, Numerische Mathematik, vol.28, issue.1, pp.93-119, 2007.
DOI : 10.1007/BFb0058774

M. E. Gage, Curve shortening makes convex curves circular, Inventiones Mathematicae, vol.86, issue.No. 1, pp.357-364, 1984.
DOI : 10.1007/BF01388602

Y. Giga, Surface evolution equations. A level set approach, Monographs in Mathematics, vol.99, 2006.

M. E. Gage and R. S. Hamilton, The heat equation shrinking convex plane curves, Journal of Differential Geometry, vol.23, issue.1, pp.69-96, 1986.
DOI : 10.4310/jdg/1214439902

C. Gerhardt, Flow of nonconvex hypersurfaces into spheres, Journal of Differential Geometry, vol.32, issue.1, pp.299-314, 1990.
DOI : 10.4310/jdg/1214445048

C. Geuzaine and J. Remacle, Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities, International Journal for Numerical Methods in Engineering, vol.69, issue.4, pp.1309-1331, 2009.
DOI : 10.1007/978-3-642-59223-2

D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Classics in Mathematics, vol.224, 2001.

M. Grayson, The heat equation shrinks embedded plane curves to round points, Journal of Differential Geometry, vol.26, issue.2, pp.285-314, 1987.
DOI : 10.4310/jdg/1214441371

F. Hecht, New development in freefem++, Journal of Numerical Mathematics, vol.20, issue.3-4, 2012.
DOI : 10.1515/jnum-2012-0013

URL : https://hal.archives-ouvertes.fr/hal-01476313

G. Huisken, Flow by mean curvature of convex surfaces into spheres, Journal of Differential Geometry, vol.20, issue.1, pp.117-138, 1984.
DOI : 10.4310/jdg/1214438998

G. Huisken and T. Ilmanen, The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality, Journal of Differential Geometry, vol.59, issue.3, pp.353-437, 2001.
DOI : 10.4310/jdg/1090349447

URL : https://doi.org/10.4310/jdg/1090349447

H. Kröner, Approximation rates for regularized level set power mean curvature flow, Portugaliae Mathematica, vol.74, issue.2
DOI : 10.4171/PM/1995

R. V. Kohn and S. Serfaty, A deterministic-control-based approach motion by curvature, Communications on Pure and Applied Mathematics, vol.52, issue.3, pp.344-407, 2006.
DOI : 10.1090/pspum/054.1/1216584

URL : http://ima.umn.edu/talks/workshops/W10.25-29.04/kohn/kohn-serfaty-cpam.pdf

R. Malladi and J. A. Sethian, Level set methods for curvature flow, image enhancement, and shape recovery in medical images Evolution of plane curves driven by a nonlinear function of curvature and anisotropy, Visualization and Mathematics . Experiments, Simulation and Environments SIAM Journal on Applied Mathematics, issue.5, pp.329-345, 1997.

H. Mitake, On convergence rates for solutions of approximate mean curvature equations, Proceedings of the American Mathematical Society, pp.3691-3696, 2011.
DOI : 10.1090/S0002-9939-2011-11002-5

R. H. Nochetto and C. Verdi, Convergence Past Singularities for a Fully Discrete Approximation of Curvature-Driven Interfaces, SIAM Journal on Numerical Analysis, vol.34, issue.2, pp.490-512, 1997.
DOI : 10.1137/S0036142994269526

K. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Applied Mathematical Sciences, vol.153, 2003.
DOI : 10.1115/1.1760520

K. 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, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

. Pdelab, URL: http://www.dune-project.org/pdelab/index, 2014.

G. Sapiro and A. Tannenbaum, On Affine Plane Curve Evolution, Journal of Functional Analysis, vol.119, issue.1, pp.79-120, 1994.
DOI : 10.1006/jfan.1994.1004

URL : https://doi.org/10.1006/jfan.1994.1004

F. Schulze, Evolution of convex hypersurfaces by powers of the mean curvature, Mathematische Zeitschrift, vol.33, issue.4, pp.721-733, 2005.
DOI : 10.1007/s00209-004-0721-5

F. Schulze, Nonlinear evolution by mean curvature and isoperimetric inequalities, Journal of Differential Geometry, vol.79, issue.2, pp.197-241, 2008.
DOI : 10.4310/jdg/1211512640

URL : http://arxiv.org/pdf/math/0606675

F. Schulze and O. Schnürer, Convexity estimates for flows by powers of the mean curvature, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.5, issue.5 2, pp.261-277, 2006.

J. A. Sethian, Theory, algorithms, and applications of level set methods for propagating interfaces, Acta Numerica, vol.11, pp.309-395, 1996.
DOI : 10.1007/BF00133570

J. A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge Monographs on Applied and Computational Mathematics, vol.3, 1999.

C. G. Simader, On Dirichlet's Boundary Value Problem, Lecture Notes in Math. v, vol.268, 1972.
DOI : 10.1007/BFb0058774

I. Toulopoulos and T. Wick, Numerical Methods for Power-Law Diffusion Problems, SIAM Journal on Scientific Computing, vol.39, issue.3, pp.681-710, 2017.
DOI : 10.1137/16M1067792

N. J. Walkington, Algorithms for Computing Motion by Mean Curvature, SIAM Journal on Numerical Analysis, vol.33, issue.6, pp.2215-2238, 1996.
DOI : 10.1137/S0036142994262068

URL : http://repository.cmu.edu/cgi/viewcontent.cgi?article=1505&context=math