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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
  • 46R. Abgrall.

    A review of residual distribution schemes for hyperbolic and parabolic problems: the July 2010 state of the art, in: Commun. Comput. Phys., 2012, vol. 11, no 4, pp. 1043–1080.

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  • 47R. Abgrall, G. Baurin, A. Krust, D. de Santis, M. Ricchiuto.

    Numerical approximation of parabolic problems by residual distribution schemes, in: Internat. J. Numer. Methods Fluids, 2013, vol. 71, no 9, pp. 1191–1206.

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    Construction of very high order residual distribution schemes for steady inviscid flow problems on hybrid unstructured meshes, in: J. Comput. Phys., 2011, vol. 230, no 11, pp. 4103–4136.

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    A simple construction of very high order non-oscillatory compact schemes on unstructured meshes, in: Comput. & Fluids, 2009, vol. 38, no 7, pp. 1314–1323.

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    Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structure, in: Adv. Math. Sci. Appl., 2009, vol. 19, pp. 109-129.
  • 51T. Aiki, A. Muntean.

    A free-boundary problem for concrete carbonation: front nucleation and rigorous justification of the t-law of propagation, in: Interfaces Free Bound., 2013, vol. 15, no 2, pp. 167–180.

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    A posteriori estimators for vertex centred finite volume discretization of a convection-diffusion-reaction equation arising in flow in porous media, in: Internat. J. Numer. Methods Fluids, 2009, vol. 59, no 3, pp. 259–284.

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    A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations, in: J. Comput. Phys., 2011, vol. 230, no 22, pp. 7988–8009.

    http://dx.doi.org/10.1016/j.jcp.2011.06.032
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    Corrosion modelling of iron based alloy in nuclear waste repository, in: Electrochim. Acta, 2010, vol. 55, no 15, pp. 4451–4467.
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  • 58A. Beccantini, E. Studer, S. Gounand, J.-P. Magnaud, T. Kloczko, C. Corre, S. Kudriakov.

    Numerical simulations of a transient injection flow at low Mach number regime, in: Internat. J. Numer. Methods Engrg., 2008, vol. 76, no 5, pp. 662–696.

    http://dx.doi.org/10.1002/nme.2331
  • 59L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini, A. Russo.

    Basic principles of virtual element methods, in: Math. Models Methods Appl. Sci. (M3AS), 2013, vol. 23, no 1, pp. 199–214.
  • 60J.-D. Benamou, G. Carlier, M. Laborde.

    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.

    https://doi.org/10.1051/proc/201654001
  • 61S. Berrone, V. Garbero, M. Marro.

    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.

    http://dx.doi.org/10.1016/j.compfluid.2010.08.014
  • 62C. Besse.

    Analyse numérique des systèmes de Davey–Stewartson, Université Bordeaux 1, 1998.
  • 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.
  • 66C. Calgaro, E. Creusé, T. Goudon.

    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
  • 68C. Cancès, T. O. Gallouët, L. Monsaingeon.

    Incompressible immiscible multiphase flows in porous media: a variational approach, in: Anal. PDE, 2017, vol. 10, no 8, pp. 1845–1876.

    https://doi.org/10.2140/apde.2017.10.1845
  • 69C. Cancès, C. Guichard.

    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.

    http://dx.doi.org/10.1142/S021820251150028X
  • 75E. Creusé, S. Nicaise, Z. Tang, Y. Le Menach, N. Nemitz, F. Piriou.

    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.
  • 76E. Creusé, S. Nicaise, E. Verhille.

    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
  • 77R. Danchin, X. Liao.

    On the well-posedness of the full low Mach number limit system in general critical Besov spaces, in: Commun. Contemp. Math., 2012, vol. 14, no 3, 1250022, 47 p.

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  • 78D. 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: Comput. Methods Appl. Math., 2014, vol. 14, no 4, pp. 461–472.

    https://doi.org/10.1515/cmam-2014-0018
  • 79D. A. Di Pietro, M. Vohralík.

    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).
  • 80J. Dolbeault, C. Mouhot, C. Schmeiser.

    Hypocoercivity for linear kinetic equations conserving mass, in: Trans. Amer. Math. Soc., 2015, vol. 367, no 6, pp. 3807–3828.

    https://doi.org/10.1090/S0002-9947-2015-06012-7
  • 81V. Dolejší, A. Ern, M. Vohralík.

    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.

    http://dx.doi.org/10.1137/110859282
  • 82D. Donatelli, E. Feireisl, P. Marcati.

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    Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods, in: Numer. Math., 2008, vol. 111, no 1, pp. 121–158.

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