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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 2, pp. 651–680. [ DOI : 10.1007/s00205-014-0839-5 ]
  https://hal.archives-ouvertes.fr/hal-00848547

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 11A. Zurek.
  Free boundary problems for the degradation of materials and biofilms growth: numerical analysis and modelisation, Université de Lille, September 2019.
  https://tel.archives-ouvertes.fr/tel-02397231
• 12c. colin.
  Analysis and numerical simulation by a combined Finite Volumes - Finite Elements method of low Mach type models, Université de Lille / Laboratoire Paul Painlevé, May 2019.
  https://hal.archives-ouvertes.fr/tel-02406716

Articles in International Peer-Reviewed Journals

• 13A. Ait Hammou Oulhaj, C. Cancès, C. Chainais-Hillairet, P. Laurençot.
  Large time behavior of a two phase extension of the porous medium equation, in: Interfaces and Free Boundaries, 2019, vol. 21, pp. 199-229, https://arxiv.org/abs/1803.10476. [ DOI : 10.4171/IFB/421 ]
  https://hal.archives-ouvertes.fr/hal-01752759
• 14A. Ait Hammou Oulhaj, D. Maltese.
  Convergence of a positive nonlinear control volume finite element scheme for an anisotropic seawater intrusion model with sharp interfaces, in: Numerical Methods for Partial Differential Equations, 2020, vol. 36, n^o 1, pp. 133-153. [ DOI : 10.1002/num.22422 ]
  https://hal.archives-ouvertes.fr/hal-01906872
• 15C. Besse, S. Descombes, G. Dujardin, I. Lacroix-Violet.
  Energy preserving methods for nonlinear Schrödinger equations, in: IMA Journal of Numerical Analysis, 2019, forthcoming. [ DOI : 10.1016/j.apnum.2019.11.008 ]
  https://hal.archives-ouvertes.fr/hal-01951527
• 16M. Bessemoulin-Chatard, C. Chainais-Hillairet.
  Uniform-in-time Bounds for approximate Solutions of the drift-diffusion System, in: Numerische Mathematik, 2019, vol. 141, n^o 4, pp. 881-916. [ DOI : 10.1007/s00211-018-01019-1 ]
  https://hal.archives-ouvertes.fr/hal-01659418
• 17M. Bessemoulin-Chatard, M. Herda, T. Rey.
  Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations, in: Mathematics of Computation, September 2019, 39 pages. [ DOI : 10.1090/mcom/3490 ]
  https://hal.archives-ouvertes.fr/hal-01957832
• 18O. Blondel, C. Cancès, M. Sasada, M. Simon.
  Convergence of a Degenerate Microscopic Dynamics to the Porous Medium Equation, in: Annales de l'Institut Fourier, 2019, forthcoming.
  https://hal.archives-ouvertes.fr/hal-01710628
• 19D. Bresch, M. Gisclon, I. Lacroix-Violet.
  On Navier-Stokes-Korteweg and Euler-Korteweg Systems: Application to Quantum Fluids Models, in: Archive for Rational Mechanics and Analysis, 2019, vol. 233, n^o 3, pp. 975-1025, https://arxiv.org/abs/1703.09460. [ DOI : 10.1007/s00205-019-01373-w ]
  https://hal.archives-ouvertes.fr/hal-01496960
• 20C. Calgaro, C. Colin, E. Creusé.
  A combined finite volume - finite element scheme for a low-Mach system involving a Joule term, in: AIMS Mathematics, 2019, vol. 5, n^o 1, pp. 311-331, forthcoming.
  https://hal.archives-ouvertes.fr/hal-02398893
• 21C. Calgaro, c. colin, E. Creusé.
  A combined Finite Volumes -Finite Elements method for a low-Mach model, in: International Journal for Numerical Methods in Fluids, 2019, vol. 90, n^o 1, pp. 1-21. [ DOI : 10.1002/fld.4706 ]
  https://hal.archives-ouvertes.fr/hal-01574894
• 22C. 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, 2019, vol. 42, n^o 1, pp. 250-271. [ DOI : 10.1002/mma.5342 ]
  https://hal.archives-ouvertes.fr/hal-01801242
• 23C. 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, 2019, vol. 35, n^o 2, pp. 545-575, https://arxiv.org/abs/1801.09408. [ DOI : 10.1002/num.22313 ]
  https://hal.archives-ouvertes.fr/hal-01695129
• 24C. 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, 2019, vol. 30, n^o 6, pp. 1123-1152. [ DOI : 10.1017/S0956792518000633 ]
  https://hal.archives-ouvertes.fr/hal-01700952
• 25C. Cancès, D. Matthes, F. Nabet.
  A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow, in: Archive for Rational Mechanics and Analysis, 2019, vol. 233, n^o 2, pp. 837–866. [ DOI : 10.1007/s00205-019-01369-6 ]
  https://hal.archives-ouvertes.fr/hal-01665338
• 26C. Chainais-Hillairet, M. Herda.
  Large-time behaviour of a family of finite volume schemes for boundary-driven convection-diffusion equations, in: IMA Journal of Numerical Analysis, November 2019, https://arxiv.org/abs/1810.01087, forthcoming. [ DOI : 10.1093/imanum/drz037 ]
  https://hal.archives-ouvertes.fr/hal-01885015
• 27A. Chambolle, L. A. D. Ferrari, B. Merlet.
  A phase-field approximation of the Steiner problem in dimension two, in: Advances in Calculus of Variation, 2019, vol. 12, n^o 2, pp. 157–179, https://arxiv.org/abs/1609.00519v1 - 27 pages, 8 figures. [ DOI : 10.1515/acv-2016-0034 ]
  https://hal.archives-ouvertes.fr/hal-01359483
• 28A. Chambolle, L. A. D. Ferrari, B. Merlet.
  Strong approximation in h-mass of rectifiable currents under homological constraint, in: Advances in Calculus of Variation, 2019, https://arxiv.org/abs/1806.05046, forthcoming. [ DOI : 10.1515/acv-2018-0079 ]
  https://hal.archives-ouvertes.fr/hal-01813234
• 29A. 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, 2019, vol. 25 (2019), n^o 43, 39 p, https://arxiv.org/abs/1710.08808, forthcoming.
  https://hal.archives-ouvertes.fr/hal-01622540
• 30M. Cicuttin, A. Ern, S. Lemaire.
  A Hybrid High-Order method for highly oscillatory elliptic problems, in: Computational Methods in Applied Mathematics, 2019, vol. 19, n^o 4, pp. 723-748. [ DOI : 10.1515/cmam-2018-0013 ]
  https://hal.archives-ouvertes.fr/hal-01467434
• 31E. Creusé, P. Dular, S. Nicaise.
  About the gauge conditions arising in Finite Element magnetostatic problems, in: Computers and Mathematics with Applications, 2019, vol. 77, n^o 6, pp. 1563-1582.
  https://hal.archives-ouvertes.fr/hal-01955649
• 32E. 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, 2019, vol. 77, n^o 6, pp. 1549-1562.
  https://hal.archives-ouvertes.fr/hal-01955692
• 33M. Goldman, B. Merlet.
  Recent results on non-convex functionals penalizing oblique oscillations, in: Rendiconti del Seminario Matematico, 2019.
  https://hal.archives-ouvertes.fr/hal-02382214
• 34M. Goldman, B. Merlet, V. Millot.
  A Ginzburg-Landau model with topologically induced free discontinuities, in: Annales de l'Institut Fourier, 2019, forthcoming.
  https://hal.archives-ouvertes.fr/hal-01643795
• 35M. Herda, L. M. Rodrigues.
  Anisotropic Boltzmann-Gibbs dynamics of strongly magnetized Vlasov-Fokker-Planck equations, in: Kinetic and Related Models , 2019, vol. 12, n^o 3, pp. 593-636, https://arxiv.org/abs/1610.05138. [ DOI : 10.3934/krm.2019024 ]
  https://hal.archives-ouvertes.fr/hal-01382854
• 36S. Lemaire.
  Bridging the Hybrid High-Order and Virtual Element methods, in: IMA Journal of Numerical Analysis, 2019, forthcoming.
  https://hal.archives-ouvertes.fr/hal-01902962
• 37W. Melis, T. Rey, G. Samaey.
  Projective and telescopic projective integration for the nonlinear BGK and Boltzmann equations, in: SMAI Journal of Computational Mathematics, 2019, vol. 5, pp. 53-88, https://arxiv.org/abs/1712.06362. [ DOI : 10.5802/smai-jcm.43 ]
  https://hal.archives-ouvertes.fr/hal-01666346
• 38N. Peton, C. Cancès, D. Granjeon, Q.-H. Tran, S. Wolf.
  Numerical scheme for a water flow-driven forward stratigraphic model, in: Computational Geosciences, 2019, forthcoming. [ DOI : 10.1007/s10596-019-09893-w ]
  https://hal.archives-ouvertes.fr/hal-01870347
• 39A. Zurek.
  Numerical approximation of a concrete carbonation model: study of the $\sqrt{t}$-law of propagation, in: Numerical Methods for Partial Differential Equations, May 2019, vol. 35, n^o 5, pp. 1801-1820. [ DOI : 10.1002/num.22377 ]
  https://hal.archives-ouvertes.fr/hal-01839277

International Conferences with Proceedings

• 40M. Cicuttin, A. Ern, S. Lemaire.
  On the implementation of a multiscale Hybrid High-Order method, in: ENUMATH 2017, Bergen, Norway, I. Berre, K. Kumar, J. M. Nordbotten, I. S. Pop, F. A. Radu (editors), Numerical Mathematics and Advanced Applications - ENUMATH 2017, Springer, Cham, 2019, vol. 126, pp. 509-517. [ DOI : 10.1007/978-3-319-96415-7_46 ]
  https://hal.archives-ouvertes.fr/hal-01661925
• 41D. Matthes, C. Cancès, F. Nabet.
  A degenerate Cahn‐Hilliard model as constrained Wasserstein gradient flow, in: GAMM annual meeting, Vienna, Austria, International Association for Applied Mathematics and Mechanics, November 2019, vol. 19, n^o 1. [ DOI : 10.1002/pamm.201900158 ]
  https://hal.archives-ouvertes.fr/hal-02377146

Software

• 42A. Mouton, C. Calgaro, E. Creusé.
  NS2DDV - Navier-Stokes 2D à Densité Variable, September 2019,
  [ SWH-ID : swh:1:dir:a126af9f1534e0b9f3431531a5f4751ad9b7b2fe ], Software.
  https://hal.archives-ouvertes.fr/hal-02137040

Other Publications

• 43F. Alouges, A. de Bouard, B. Merlet, L. Nicolas.
  Stochastic homogenization of the Landau-Lifshitz-Gilbert equation, February 2019, https://arxiv.org/abs/1902.05743 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02020241
• 44N. Ayi, M. Herda, H. Hivert, I. Tristani.
  A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium, December 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02389146
• 45S. Billiard, M. Derex, L. Maisonneuve, T. Rey.
  Convergence of knowledge in a cultural evolution model with population structure, random social learning and credibility biases, November 2019, 25 pages.
  https://hal.archives-ouvertes.fr/hal-02357188
• 46C. Calgaro, E. Creusé.
  A finite volume method for a convection- diffusion equation involving a Joule term, 2019, working paper or preprint.
  https://hal.inria.fr/hal-02432936
• 47M. Campos Pinto, F. Charles, B. Després, M. Herda.
  A projection algorithm on the set of polynomials with two bounds, May 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02128851
• 48C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, B. Gaudeul.
  A numerical analysis focused comparison of several Finite Volume schemes for an Unipolar Degenerated Drift-Diffusion Model, December 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02194604
• 49C. Cancès, C. Chainais-Hillairet, M. Herda, S. Krell.
  Large time behavior of nonlinear finite volume schemes for convection-diffusion equations, November 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02360155
• 50C. Cancès, T. O. Gallouët, G. Todeschi.
  A variational finite volume scheme for Wasserstein gradient flows, July 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02189050
• 51C. Cancès, B. Gaudeul.
  Entropy diminishing finite volume approximation of a cross-diffusion system, 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02418908
• 52C. Cancès, D. Maltese.
  A gravity current model with capillary trapping for oil migration in multilayer geological basins, August 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02272965
• 53C. Cancès, F. Nabet.
  Energy stable discretization for two-phase porous media flows, January 2020, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02442233
• 54C. Cancès, F. Nabet, M. Vohralík.
  Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations, January 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01894884
• 55C. Chainais-Hillairet, M. Herda.
  $L^{\infty }$ bounds for numerical solutions of noncoercive convection-diffusion equations, December 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02404546
• 56C. Chainais-Hillairet, S. Krell.
  Exponential decay to equilibrium of nonlinear DDFV schemes for convection-diffusion equations, December 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02408212
• 57F. Chave.
  Numerical study of the fracture diffusion-dispersion coefficient for passive transport in fractured porous media, December 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02412691
• 58F. Chave, D. A. Di Pietro, S. Lemaire.
  A three-dimensional Hybrid High-Order method for magnetostatics, December 2019, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02407175
• 59B. Després, M. Herda.
  Computation of sum of squares polynomials from data points, August 2019, https://arxiv.org/abs/1812.02444 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01946539
• 60G. Dujardin, I. Lacroix-Violet.
  High order linearly implicit methods for evolution equations: How to solve an ODE by inverting only linear systems, November 2019, https://arxiv.org/abs/1911.06016 - working paper or preprint.
  https://hal.inria.fr/hal-02361814
• 61A. El Keurti, T. Rey.
  Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions, December 2019, https://arxiv.org/abs/1912.06423 - 8 pages.
  https://hal.archives-ouvertes.fr/hal-02408246
• 62M. Goldman, B. Merlet.
  Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimates, May 2019, https://arxiv.org/abs/1905.07905 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-02132896

References in notes

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• 78C. Besse.
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• 79M. 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, n^o 4.
  https://epubs.siam.org/doi/abs/10.1137/130913432
• 80D. 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.
• 81C. Calgaro, E. Creusé, T. Goudon.
  An hybrid finite volume-finite element method for variable density incompressible flows, in: J. Comput. Phys., 2008, vol. 227, n^o 9, pp. 4671–4696.
• 82C. 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
• 83C. 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, n^o 298, pp. 549-580.
  https://hal.archives-ouvertes.fr/hal-00955091
• 84C. 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, n^o 285, pp. 153–188.
  http://dx.doi.org/10.1090/S0025-5718-2013-02723-8
• 85J. 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, n^o 1, pp. 1–82.
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• 86C. 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.
• 87C. 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, n^o 1, pp. 135-162.
  https://hal.archives-ouvertes.fr/hal-00924282
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