P. Barq, J. M. Haudin, J. Agassant, H. Roth, and P. Bourgin, Instability Phenomena in Film Casting Process, International Polymer Processing, vol.5, issue.4, pp.264-271, 2014.
DOI : 10.3139/217.900264

Y. Demay and J. Agassant, An Overview of Molten Polymer Drawing Instabilities, International Polymer Processing, vol.29, issue.1, pp.128-139, 2014.
DOI : 10.3139/217.2832
URL : https://hal.archives-ouvertes.fr/hal-00961422

J. Pearson, Mechanical principles of polymer melt processing, 1966.

R. Fisher and M. Denn, Finite-amplitude stability and draw resonance in isothermal melt spinning, Chemical Engineering Science, vol.30, issue.9, pp.1129-1134, 1975.
DOI : 10.1016/0009-2509(75)87015-1

S. D. 'halewyn, J. Agassant, and Y. Demay, Numerical simulation of the cast film process, Polym. Eng. Sci, vol.30, pp.335-340, 1990.

D. Silagy, Y. Demay, and J. Agassant, Stationary and stability analysis of the film casting process, Journal of Non-Newtonian Fluid Mechanics, vol.79, issue.2-3, pp.563-583, 1998.
DOI : 10.1016/S0377-0257(98)00119-0
URL : https://hal.archives-ouvertes.fr/hal-00613102

B. Debbaut, J. Marchal, and M. Crochet, Viscoelastic effects in film casting, Z. angew. Math. Phys, vol.46, pp.5679-5698, 1995.
DOI : 10.1007/978-3-0348-9229-2_35

J. Kim, J. Lee, D. Shin, and H. Jung, Transient solutions of the dynamics of film casting process using a 2-D viscoelastic model, Journal of Non-Newtonian Fluid Mechanics, vol.132, issue.1-3, pp.53-60, 2005.
DOI : 10.1016/j.jnnfm.2005.10.002

D. Shin, J. Lee, J. Kim, and H. Jung, Transient and steady-state solutions of 2D viscoelastic nonisothermal simulation model of film casting process via finite element method, Journal of Rheology, vol.51, issue.3, pp.393-407, 2007.
DOI : 10.1122/1.2714781

M. Souli, Y. Demay, and A. Habbal, Finite-element study of the draw resonance instability, European journal of mechanics. B, Fluids, vol.12, issue.1, pp.1-13, 1998.

A. Fortin, P. Carrier, and Y. Demay, Numerical simulation of coextrusion and film casting, International Journal for Numerical Methods in Fluids, vol.141, issue.1, pp.31-57, 1995.
DOI : 10.1002/fld.1650200103

Y. Yeow, On the stability of extending films: a model for the film casting process, Journal of Fluid Mechanics, vol.8, issue.03, pp.613-622, 1974.
DOI : 10.1007/BF01973479

A. Ern and J. Guermond, ´ Eléments finis: théorie, applications, mise en oeuvre, 2000.

D. Arnold, F. Brezzi, and M. Fortin, A stable finite element for the stokes equations, Calcolo, vol.21, issue.4, pp.337-344, 1984.
DOI : 10.1007/BF02576171

E. Mitsoulis and J. Vlachopoulos, Simulation of extrudate swell from long slit and capillary dies, Polym. Proc. Eng, vol.2, p.153, 1984.

B. Cockburn, Discontinuous galerkin methods for convection dominated problems, Lecture notes of the NASA/VKI Summer School on High Order Discretization Methods in Comp. Fluid Dynamics, 1998.

C. Bernardi, Y. Maday, and A. Patera, A new nonconforming approach to domain decomposition: the mortar element method Non linear partial differential equations and their applications, 1992.

F. and B. Belgacem, The Mixed Mortar Finite Element Method for the Incompressible Stokes Problem: Convergence Analysis, SIAM Journal on Numerical Analysis, vol.37, issue.4, pp.1085-1100, 2000.
DOI : 10.1137/S0036142997329220

C. Canuto, M. Hussaini, A. Quarteroni, and T. Zang, Spectral Methods, 2007.
DOI : 10.1002/0470091355.ecm003m
URL : https://hal.archives-ouvertes.fr/hal-01296839

T. Tezduyar, Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.23-24, pp.2983-3000, 2006.
DOI : 10.1016/j.cma.2004.09.018

E. Hachem, G. Francois, and T. Coupez, Stabilised Finite Element for high Reynolds number, LES and free surface flow problems, No. 15 in Navier-Stokes Equations: Properties, Description and Applications, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00671091

M. Sussman, P. Smereka, and S. Osher, A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow, Journal of Computational Physics, vol.114, issue.1, pp.146-159, 1994.
DOI : 10.1006/jcph.1994.1155

L. Ville, L. Silva, and T. Coupez, Convected level set method for the numerical simulation of fluid buckling, International Journal for Numerical Methods in Fluids, vol.4, issue.3, pp.324-344, 2010.
DOI : 10.1002/fld.2259
URL : https://hal.archives-ouvertes.fr/hal-00595325

S. Osher and R. Fedkiw, Level Set Methods: An Overview and Some Recent Results, Journal of Computational Physics, vol.169, issue.2, pp.453-502, 2001.
DOI : 10.1006/jcph.2000.6636

J. Sethian, Level Set Methods and Fast Marching Methods : Evoloving Interfaces in Computational Geometry,Fluid Mechanics, Computer Vision, and Materials Science, 1999.

A. Brooks and T. Hughes, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, vol.32, issue.1-3, pp.199-259, 1982.
DOI : 10.1016/0045-7825(82)90071-8

T. Coupez and E. Hachem, Solution of high-Reynolds incompressible flow with stabilized finite element and adaptive anisotropic meshing, Computer Methods in Applied Mechanics and Engineering, vol.267, pp.65-85, 2013.
DOI : 10.1016/j.cma.2013.08.004
URL : https://hal.archives-ouvertes.fr/hal-00866734