Project-Team Rapsodi
Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Dissemination
Bibliography
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Bibliography

Major publications by the team in recent years
  • 1M. Bessemoulin-Chatard, C. Chainais-Hillairet.
    Exponential decay of a finite volume scheme to the thermal equilibrium for drift–diffusion systems, in: Journal of Numerical Mathematics, 2017, vol. 25, no 3, pp. 147-168. [ DOI : 10.1515/jnma-2016-0007 ]
    https://hal.archives-ouvertes.fr/hal-01250709
  • 2C. Calgaro, E. Creusé, T. Goudon, S. Krell.
    Simulations of non homogeneous viscous flows with incompressibility constraints, in: Mathematics and Computers in Simulation, 2017, vol. 137, pp. 201-225.
    https://hal.archives-ouvertes.fr/hal-01246070
  • 3C. Cancès, T. Gallouët, L. Monsaingeon.
    Incompressible immiscible multiphase flows in porous media: a variational approach, in: Analysis & PDE, 2017, vol. 10, no 8, pp. 1845–1876. [ DOI : 10.2140/apde.2017.10.1845 ]
    https://hal.archives-ouvertes.fr/hal-01345438
  • 4C. Cancès, C. Guichard.
    Numerical analysis of a robust free energy diminishing Finite Volume scheme for parabolic equations with gradient structure, in: Foundations of Computational Mathematics, 2017, vol. 17, no 6, pp. 1525-1584.
    https://hal.archives-ouvertes.fr/hal-01119735
  • 5C. Chainais-Hillairet, B. Merlet, A. Vasseur.
    Positive Lower Bound for the Numerical Solution of a Convection-Diffusion Equation, in: FVCA8 2017 - International Conference on Finite Volumes for Complex Applications VIII, Lille, France, Springer, June 2017, pp. 331-339. [ DOI : 10.1007/978-3-319-57397-7_26 ]
    https://hal.archives-ouvertes.fr/hal-01596076
  • 6D. A. Di Pietro, A. Ern, S. Lemaire.
    An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators, in: Computational Methods in Applied Mathematics, June 2014, vol. 14, no 4, pp. 461-472. [ DOI : 10.1515/cmam-2014-0018 ]
    https://hal.archives-ouvertes.fr/hal-00978198
  • 7G. Dimarco, R. Loubère, J. Narski, T. Rey.
    An efficient numerical method for solving the Boltzmann equation in multidimensions, in: Journal of Computational Physics, 2018, vol. 353, pp. 46-81. [ DOI : 10.1016/j.jcp.2017.10.010 ]
    https://hal.archives-ouvertes.fr/hal-01357112
  • 8F. Filbet, M. Herda.
    A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure, in: Numerische Mathematik, 2017, vol. 137, no 3, pp. 535-577.
    https://hal.archives-ouvertes.fr/hal-01326029
  • 9I. Lacroix-Violet, A. Vasseur.
    Global weak solutions to the compressible quantum Navier–Stokes equation and its semi-classical limit, in: Journal de Mathématiques Pures et Appliquées, 2018, vol. 114, pp. 191-210.
    https://hal.archives-ouvertes.fr/hal-01347943
  • 10B. Merlet.
    A highly anisotropic nonlinear elasticity model for vesicles I. Eulerian formulation, rigidity estimates and vanishing energy limit, in: Arch. Ration. Mech. Anal., 2015, vol. 217, no 2, pp. 651–680. [ DOI : 10.1007/s00205-014-0839-5 ]
    https://hal.archives-ouvertes.fr/hal-00848547
Publications of the year

Articles in International Peer-Reviewed Journals

  • 11A. Ait Hammou Oulhaj.
    Numerical analysis of a finite volume scheme for a seawater intrusion model with cross-diffusion in an unconfined aquifer, in: Numerical Methods for Partial Differential Equations, May 2018. [ DOI : 10.1002/num.22234 ]
    https://hal.archives-ouvertes.fr/hal-01432197
  • 12A. Ait Hammou Oulhaj, C. Cancès, C. Chainais-Hillairet.
    Numerical analysis of a nonlinearly stable and positive Control Volume Finite Element scheme for Richards equation with anisotropy, in: ESAIM: Mathematical Modelling and Numerical Analysis, 2018, vol. 52, no 4, pp. 1532-1567. [ DOI : 10.1051/m2an/2017012 ]
    https://hal.archives-ouvertes.fr/hal-01372954
  • 13M. Bessemoulin-Chatard, C. Chainais-Hillairet.
    Uniform-in-time Bounds for approximate Solutions of the drift-diffusion System, in: Numerische Mathematik, 2018.
    https://hal.archives-ouvertes.fr/hal-01659418
  • 14C. Calgaro, c. colin, E. Creusé, E. Zahrouni.
    Approximation by an iterative method of a low Mach model with temperature dependent viscosity, in: Mathematical Methods in the Applied Sciences, 2018. [ DOI : 10.1002/mma.5342 ]
    https://hal.archives-ouvertes.fr/hal-01801242
  • 15C. Calgaro, M. Ezzoug, E. Zahrouni.
    Stability and convergence of an hybrid finite volume-finite element method for a multiphasic incompressible fluid model, in: Communications on Pure and Applied Analysis, March 2018, vol. 17, no 2, pp. 429-448.
    https://hal.archives-ouvertes.fr/hal-01586201
  • 16C. Cancès.
    Energy stable numerical methods for porous media flow type problems, in: Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles, 2018, vol. 73, 78 p. [ DOI : 10.2516/ogst/2018067 ]
    https://hal.archives-ouvertes.fr/hal-01953395
  • 17C. Cancès, C. Chainais-Hillairet, A. Gerstenmayer, A. Jüngel.
    Convergence of a Finite-Volume Scheme for a Degenerate Cross-Diffusion Model for Ion Transport, in: Numerical Methods for Partial Differential Equations, 2018, https://arxiv.org/abs/1801.09408.
    https://hal.archives-ouvertes.fr/hal-01695129
  • 18C. Cancès, C. Chainais-Hillairet, S. Krell.
    Numerical analysis of a nonlinear free-energy diminishing Discrete Duality Finite Volume scheme for convection diffusion equations, in: Computational Methods in Applied Mathematics, 2018, vol. 18, no 3, pp. 407-432, https://arxiv.org/abs/1705.10558 - Special issue on "Advanced numerical methods: recent developments, analysis and application". [ DOI : 10.1515/cmam-2017-0043 ]
    https://hal.archives-ouvertes.fr/hal-01529143
  • 19C. Cancès, T. Gallouët, M. Laborde, L. Monsaingeon.
    Simulation of multiphase porous media flows with minimizing movement and finite volume schemes, in: European Journal of Applied Mathematics, 2018. [ DOI : 10.1017/S0956792518000633 ]
    https://hal.archives-ouvertes.fr/hal-01700952
  • 20C. Chainais-Hillairet, B. Merlet, A. Zurek.
    Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation, in: ESAIM: Mathematical Modelling and Numerical Analysis, June 2018, vol. 52, no 2, pp. 457-480.
    https://hal.archives-ouvertes.fr/hal-01477543
  • 21A. Chambolle, L. A. D. Ferrari, B. Merlet.
    Variational approximation of size-mass energies for k-dimensional currents, in: ESAIM: Control, Optimisation and Calculus of Variations, April 2018, https://arxiv.org/abs/1710.08808.
    https://hal.archives-ouvertes.fr/hal-01622540
  • 22M. Cicuttin, A. Ern, S. Lemaire.
    A Hybrid High-Order method for highly oscillatory elliptic problems, in: Computational Methods in Applied Mathematics, 2018. [ DOI : 10.1515/cmam-2018-0013 ]
    https://hal.archives-ouvertes.fr/hal-01467434
  • 23E. Creusé, P. Dular, S. Nicaise.
    About the gauge conditions arising in Finite Element magnetostatic problems, in: Computers and Mathematics with Applications, 2018.
    https://hal.archives-ouvertes.fr/hal-01955649
  • 24E. Creusé, Y. Le Menach, S. Nicaise, F. Piriou, R. Tittarelli.
    Two Guaranteed Equilibrated Error Estimators for Harmonic Formulations in Eddy Current Problems, in: Computers and Mathematics with Applications, 2018.
    https://hal.archives-ouvertes.fr/hal-01955692
  • 25G. Dimarco, R. Loubère, J. Narski, T. Rey.
    An efficient numerical method for solving the Boltzmann equation in multidimensions, in: Journal of Computational Physics, 2018, vol. 353, pp. 46-81. [ DOI : 10.1016/j.jcp.2017.10.010 ]
    https://hal.archives-ouvertes.fr/hal-01357112
  • 26M. Herda, L. M. M. Rodrigues.
    Anisotropic Boltzmann-Gibbs dynamics of strongly magnetized Vlasov-Fokker-Planck equations, in: Kinetic and Related Models , 2018, https://arxiv.org/abs/1610.05138.
    https://hal.archives-ouvertes.fr/hal-01382854
  • 27I. Lacroix-Violet, A. Vasseur.
    Global weak solutions to the compressible quantum navier-stokes equation and its semi-classical limit, in: Journal de Mathématiques Pures et Appliquées, 2018, vol. 114, pp. 191-210, https://arxiv.org/abs/1607.06646.
    https://hal.archives-ouvertes.fr/hal-01347943
  • 28R. Tittarelli, Y. Le Menach, F. Piriou, E. Creusé, S. Nicaise, J.-P. Ducreux.
    Comparison of Numerical Error Estimators for Eddy Current Problems solved by FEM, in: IEEE Transactions on Magnetics, 2018, vol. 54, no 3.
    https://hal.archives-ouvertes.fr/hal-01645591

Other Publications

References in notes
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    Basic principles of virtual element methods, in: Math. Models Methods Appl. Sci. (M3AS), 2013, vol. 23, no 1, pp. 199–214.
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    An augmented Lagrangian approach to Wasserstein gradient flows and applications, in: Gradient flows: from theory to application, ESAIM Proc. Surveys, EDP Sci., Les Ulis, 2016, vol. 54, pp. 1–17.
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    Numerical simulation of low-Reynolds number flows past rectangular cylinders based on adaptive finite element and finite volume methods, in: Comput. & Fluids, 2011, vol. 40, pp. 92–112.
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  • 62C. Besse.
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  • 63M. Bessemoulin-Chatard, C. Chainais-Hillairet.
    Exponential decay of a finite volume scheme to the thermal equilibrium for drift-diffusion systems, in: J. Numer. Math., 2017, vol. 25, no 3, pp. 147–168.
    https://doi.org/10.1515/jnma-2016-0007
  • 64M. Bessemoulin-Chatard, C. Chainais-Hillairet, M.-H. Vignal.
    Study of a fully implicit scheme for the drift-diffusion system. Asymptotic behavior in the quasi-neutral limit, in: SIAM, J. Numer. Anal., 2014, vol. 52, no 4.
    http://epubs.siam.org/toc/sjnaam/52/4
  • 65D. Bresch, P. Noble, J.-P. Vila.
    Relative entropy for compressible Navier-Stokes equations with density dependent viscosities and various applications, in: LMLFN 2015—low velocity flows—application to low Mach and low Froude regimes, ESAIM Proc. Surveys, EDP Sci., Les Ulis, 2017, vol. 58, pp. 40–57.
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    An hybrid finite volume-finite element method for variable density incompressible flows, in: J. Comput. Phys., 2008, vol. 227, no 9, pp. 4671–4696.
  • 67C. Calgaro, E. Creusé, T. Goudon.
    Modeling and simulation of mixture flows: application to powder-snow avalanches, in: Comput. & Fluids, 2015, vol. 107, pp. 100–122.
    http://dx.doi.org/10.1016/j.compfluid.2014.10.008
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    Incompressible immiscible multiphase flows in porous media: a variational approach, in: Anal. PDE, 2017, vol. 10, no 8, pp. 1845–1876.
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    Convergence of a nonlinear entropy diminishing Control Volume Finite Element scheme for solving anisotropic degenerate parabolic equations, in: Mathematics of Computation, 2016, vol. 85, no 298, pp. 549-580.
    https://hal.archives-ouvertes.fr/hal-00955091
  • 70C. Cancès, I. S. Pop, M. Vohralík.
    An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow, in: Math. Comp., 2014, vol. 83, no 285, pp. 153–188.
    http://dx.doi.org/10.1090/S0025-5718-2013-02723-8
  • 71J. A. Carrillo, A. Jüngel, P. A. Markowich, G. Toscani, A. Unterreiter.
    Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, in: Monatsh. Math., 2001, vol. 133, no 1, pp. 1–82.
    http://dx.doi.org/10.1007/s006050170032
  • 72C. Chainais-Hillairet.
    Entropy method and asymptotic behaviours of finite volume schemes, in: Finite volumes for complex applications. VII. Methods and theoretical aspects, Springer Proc. Math. Stat., Springer, Cham, 2014, vol. 77, pp. 17–35.
  • 73C. Chainais-Hillairet, A. Jüngel, S. Schuchnigg.
    Entropy-dissipative discretization of nonlinear diffusion equations and discrete Beckner inequalities, in: Modelisation Mathématique et Analyse Numérique, 2016, vol. 50, no 1, pp. 135-162.
    https://hal.archives-ouvertes.fr/hal-00924282
  • 74E. Creusé, S. Nicaise, Z. Tang, Y. Le Menach, N. Nemitz, F. Piriou.
    Residual-based a posteriori estimators for the 𝐀-φ magnetodynamic harmonic formulation of the Maxwell system, in: Math. Models Methods Appl. Sci., 2012, vol. 22, no 5, 1150028, 30 p.
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    Residual-based a posteriori estimators for the 𝐓/Ω magnetodynamic harmonic formulation of the Maxwell system, in: Int. J. Numer. Anal. Model., 2013, vol. 10, no 2, pp. 411–429.
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    Robust equilibrated a posteriori error estimators for the Reissner-Mindlin system, in: Calcolo, 2011, vol. 48, no 4, pp. 307–335.
    http://dx.doi.org/10.1007/s10092-011-0042-0
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    https://doi.org/10.1515/cmam-2014-0018
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    A Review of Recent Advances in Discretization Methods, a Posteriori Error Analysis, and Adaptive Algorithms for Numerical Modeling in Geosciences, in: Oil & Gas Science and Technology-Rev. IFP, June 2014, pp. 1-29, (online first).
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    A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems, in: SIAM J. Numer. Anal., 2013, vol. 51, no 2, pp. 773–793.
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