Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS

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Chouly Franz

par Chouly Franz - publié le , mis à jour le

Maître de conférences - HDR
Laboratoire de Mathématiques de Besançon (LMB) UMR CNRS 6623
Institut Supérieur d’Ingénieurs de Franche-Comté (ISIFC)
Université de Franche-Comté, 16 route de Gray,
25030 Besançon cedex, France

Tel : (33/0) 3 81 66 63 28.
Fax : (33/0) 3 81 66 66 23.
Email :

Curriculum Vitae

Scientific interests

My research is focused on numerical analysis and scientific computing, with emphasis on finite element methods and boundary/interface conditions such as it occurs in fluid-structure interaction and contact/friction. It encompasses both theoretical aspects (proofs of stability and optimal convergence) and applied aspects (multi-disciplinary projects and industrial / biomedical applications).

Main applications fields are solid/fluid mechanics and biomechanics. For instance :

  • Computational contact mechanics applied to tyre simulation. It involves an industrial partnership with Michelin France, materialized by the PhD of Rabii Mlika, with CIFRE funding, co-supervised with Y. Renard (INSA Lyon) and in collaboration with J.F. Deldon and P. Hauret (Centre de Technologie Michelin).
  • A posteriori error estimation for soft-tissue biomechanics (within the framework of the CNRS multi-disciplinary project Defi Infinity "MEFASIM" granted for 2017). It involves as well an industrial partnership with TexiSense and a multi-disciplinary collaboration between mathematics, computational mechanics, biomechanics and computer science.

An overview of my research on Nitsche’s method for contact and friction is available here.

I mostly use GetFEM++ finite element library.


  1. Contributions au traitement des conditions limites et d’interface dans le cadre de la Méthode des Eléments Finis.
    F. Chouly. Habilitation à Diriger des Recherches de l’U.F.C. , Besançon, France. 12/2013.
  2. Modélisation physique des voies aériennes supérieures pour le Syndrome d’Apnées Obstructives du Sommeil.
    F. Chouly. Thèse de Doctorat de l’I.N.P.G. , Grenoble, France. 12/2005.

Post-doctoral supervision

  • Huu Phuoc Bui (2017-) Goal oriented a posteriori error estimation for hyperelastic contractile models applied to clinical biomechanics. Grant from AMIES and partnership with Marek Bucki (TexiSense, Grenoble).

PhD students

  • Raphaël Bulle. Université du Luxembourg (2017-). Efficient error-controlled multi-level Monte-Carlo methods for stochastic elasticity problems. Co-advisors : Jack Hale, Stéphane Bordas.
  • Rabii Mlika. INSA Lyon (2015-2018). Nitsche method for frictional contact and self-contact : mathematical and numerical study. Co-advisor : Yves Renard.
  • Michel Duprez. Université de Franche-Comté (2012-2015). Controllability of some parabolic systems. Co-advisor : Farid Ammar Khodja.
    webpage / document
  • Nicolas Hermant. Grenoble-INP (2011-2014). Observation, modeling and simulation of the vibrations of a vocal folds replica with application to pathological configurations. Co-advisors : Xavier Pelorson, Fabrice Silva.
    webpage / document

Preprints / submitted articles or notes

  1. Analysis of a stabilized penalty-free Nitsche method for the Brinkman, Stokes and Darcy problems.
    L. Blank, A. Caiazzo, F. Chouly, A. Lozinski & J. Mura. Submitted.
  2. Skew-symmetric Nitsche’s formulation in isogeometric analysis : Dirichlet and symmetry conditions, patch coupling and frictionless contact.
    Q. Hu, F. Chouly, G. Cheng & S.P.A. Bordas. Submitted.
  3. Quantifying discretization errors for soft-tissue simulation in computer assisted surgery : a preliminary study.
    S.P.A. Bordas, M. Bucki, F. Chouly, M. Duprez, V. Llleras, C. Lobos, A. Lozinski, P.-Y. Rohan & S. Tomar. Submitted.
  4. A stabilised finite element method for a time-dependent problem solved using a fictitious domain method.
    G.R. Barrenechea, F. Chouly & C. Gonzalez. Submitted.
  5. Computational fluid dynamics in the upper airway : comparison between different models and experimental data for a simplified geometry with major obstruction.
    F.E. Heravi, M.A. Nazari, F. Chouly, P. Perrier & Y. Payan. Submitted.

International Journals

  1. An unbiased Nitsche’s approximation of the frictional contact between two elastic structures.
    F. Chouly, R. Mlika & Y. Renard. Numer. Math. To appear.
  2. Numerical study of the vibrations of an elastic container filled with an inviscid fluid.
    N. Hermant, F. Chouly, F. Silva & P. Luizard. ZAMM Z. Angew. Math. Mech. To appear.
  3. Residual-based a posteriori error estimation for contact problems approximated by Nitsche’s method.
    F. Chouly, M. Fabre, P. Hild, J. Pousin & Y. Renard. IMA J. Numer. Anal. To appear.
  4. A clustering package for nucleotide sequences using Laplacian Eigenmaps and Gaussian Mixture Models.
    M. Bruneau, T. Mottet, S. Moulin, M. Kerbiriou, F. Chouly, S. Chrétien & C. Guyeux. Comput. Biol. Med. Vol. 93, pp 66-74, 2018.
  5. An unbiased Nitsche’s formulation of large deformation frictional contact and self-contact.
    R. Mlika, Y. Renard & F. Chouly. Comput. Methods Appl. Mech. Engrg. Vol. 325, pp. 265-288, 2017.
  6. Partial null controllability of parabolic linear systems.
    F. Ammar Khodja, F. Chouly & M. Duprez. Math. Control Relat. Fields. Vol. 6, pp.185-216, 2016.
  7. A time-parallel framework for coupling finite element and lattice Boltzmann methods.
    M. Astorino, F. Chouly & A. Quarteroni. Appl. Math. Res. Express. AMRX. Vol. 2016, pp. 24-67, 2016.
  8. A Nitsche finite element method for dynamic contact : 2. Stability of the schemes and numerical experiments.
    F. Chouly, P. Hild & Y. Renard. ESAIM : Math. Model. Numer. Anal. Vol. 49, pp. 503-528, 2015.
  9. A Nitsche finite element method for dynamic contact : 1. Semi-discrete problem analysis and time-marching schemes.
    F. Chouly, P. Hild & Y. Renard. ESAIM : Math. Model. Numer. Anal. Vol. 49, pp. 481-502, 2015.
  10. Symmetric and non-symmetric variants of Nitsche’s method for contact problems in elasticity : theory and numerical experiments.
    F. Chouly, P. Hild & Y. Renard. Math. Comp. Vol. 84, pp. 1089-1112, 2015.
  11. An adaptation of Nitsche’s method to the Tresca friction problem.
    F. Chouly. J. Math. Anal. Appl. Vol. 411 , pp. 329-339 , 2014.
  12. A Nitsche-based method for unilateral contact problems : numerical analysis.
    F. Chouly & P. Hild. SIAM J. Numer. Anal. Vol. 51, Num. 2, pp. 1295–1307, 2013.
  13. On convergence of the penalty method for unilateral contact problems.
    F. Chouly & P. Hild. Appl. Num. Math. Vol. 65, pp. 27-40, 2013.
  14. A local projection stabilized method for fictitious domains.
    G.-R. Barrenechea & F. Chouly. Appl. Math. Lett. Vol. 25, Num. 12, pp. 2071-2076, 2012.
  15. Comparison of computations of asymptotic flow models in a constricted channel.
    F. Chouly & P.-Y. Lagrée. Appl. Math. Model. Vol. 36, Num. 12, pp. 6061–6071, 2012.
  16. A Nitsche-based domain decomposition method for hypersingular integral equations.
    F. Chouly & N. Heuer. Numer. Math. Vol. 121, Num. 4, pp. 705-729, 2012.
  17. Robin based semi-implicit coupling in fluid-structure interaction : stability analysis and numerics.
    M. Astorino, F. Chouly & M.-A. Fernández. SIAM J. Sci. Comput., Vol. 31, Num. 6, pp. 4041-4065, 2009.
  18. A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations.
    G.-R. Barrenechea & F. Chouly. ZAMM Z. Angew. Math. Mech., Vol. 89, Num. 1, pp. 54-68, 2009.
  19. Modelling the human pharyngeal airway : validation of numerical simulations using in-vitro experiments.
    F. Chouly, A. Van Hirtum, P.-Y. Lagrée, X. Pelorson & Y. Payan. Med. Biol. Eng. Comput., Vol. 47, pp. 49-58, 2009.
  20. Numerical and experimental study of expiratory flow in the case of major upper airway obstructions with fluid-structure interaction.
    F. Chouly, A. Van Hirtum, P.-Y. Lagrée, X. Pelorson & Y. Payan. J. Fluid. Struct. , Vol. 24, pp. 250-269, 2008.

Conference Proceedings (in books, with peer-review)

  1. Nitsche-based finite element method for contact with Coulomb friction.
    F. Chouly, P. Hild, V. Lleras, & Y. Renard. Lect. Notes Comput. Sci. Eng. To appear.
    Proceedings of the European Conference on Numerical Mathematics and Advanced Applications ENUMATH 2017. Editor : Jan Martin Nordbotten.
  2. An overview of recent results on Nitsche’s method for contact problems.
    F. Chouly, M. Fabre, P. Hild, R. Mlika, J. Pousin & Y. Renard. Lect. Notes Comput. Sci. Eng. To appear.
    Proceedings of the UCL Workshop 2016 on Geometrically Unfitted Finite Element Methods and Applications. Editors : Stéphane Bordas, Erik Burman, Mats G. Larson and Maxim Olshanskii.
  3. Simulation of the retroglossal fluid-structure interaction during Obstructive Sleep Apnea.
    F. Chouly, A. Van Hirtum, P.-Y. Lagrée, J.-R. Paoli, X. Pelorson & Y. Payan. Lect. Notes Comput. Sci. Vol. 4072, pp. 48-57, 2006.
    Proceedings of the Third International Symposium ISBMS 2006 on Biomedical Simulation. Editors : Matthias Harders and Gábor Székely.

Notes in CRAS

  1. Parareal multi-model numerical zoom for parabolic multiscale problems.
    F. Chouly & A. Lozinski. C. R. Math. Vol. 352, Num. 6, pp. 535-540, 2014.
  2. An added-mass free semi-implicit coupling scheme for fluid-structure interaction.
    M. Astorino, F. Chouly & M.-A. Fernández. C. R. Math. Vol. 347, Num. 1-2, pp. 99-104, 2009.

Book chapter

  1. When a fluid-structure interaction keeps you awake : a physical approach to Obstructive Sleep Apnea.
    A. Van Hirtum, F. Chouly, P.-Y. Lagrée, J.-R. Paoli, Y. Payan & X. Pelorson. Chapter 2 of "Progress in Sleep Apnea Research", pp. 41-76, 2007. Editor : Robert T. Ferber. Nova Science Publishers. ISBN 1-60021-652-8.

Lecture notes

  1. Sur la prise en compte de quelques conditions aux limites avec la méthode des éléments finis.
    F. Chouly. CEL (Cours en ligne) cel-01564693.

National/international conferences (selection)

  1. Generalized local B-bar method for locking phenomenon in Reissner-Mindlin shell and skew-symmetric Nitsche method for boundary conditions imposing and patch coupling in IGA.
    Q. Hu, F. Chouly, A. Zilian, G. Cheng & S.P.A. Bordas. 7th GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry, 2017.
  2. Hydro-elastic finite element model of a vocal fold replica.
    N. Hermant, X. Pelorson, P. Luizard, F. Chouly & F. Silva. 22nd International Congress on Sound and Vibration, ICSV, 2015.
  3. Modèle éléments finis d’un pli vocal artificiel avec couplage hydro-élastique.
    N. Hermant, F. Silva, F. Chouly & X. Pelorson. 12ème Congrès Français d’Acoustique, CFA 2014, pp. 1821-1827 [N°000323], 2014.
  4. Evaluating soft tissue simulation in maxillofacial surgery using pre and post-operative CT scan.
    M. Chabanas, C. Marécaux, F. Chouly, F. Boutault & Y. Payan. 18th International Conference on Computer Assisted Radiology and Surgery, CARS 2004, ICS, Vol. 1268, pp. 419-424, 2004.
  5. In-vitro study of pharyngeal pressure losses at the origin of obstructive sleep apnea.
    A. Van Hirtum, F. Chouly, A. Teulé, Y. Payan & X. Pelorson. 25th Annual International Conference of the IEEE Engineering In Medicine And Biology Society, pp. 371-374. 2003.