Jerome Droniou

Directeur de Recherche (senior research fellow) at the CNRS (France)
Adjunct Professor (research) at Monash university (Melbourne, Australia)

Address: University of Montpellier,
Institut Montpelliérain Alexander Grothendieck (IMAG, UMR CNRS 5149),
CC 051, Place Eugène Bataillon
34090 Montpellier, FRANCE.
Email: jerome.droniou*at*umontpellier.fr, jerome.droniou*at*monash.edu,

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Research

Themes:

Theoretical and numerical analysis of partial differential equations: conception and rigorous analysis of numerical schemes on generic polytopal meshes, for linear and non-linear elliptic and parabolic models. I design analysis techniques that cover a wide range of numerical schemes (low- and high-order methods: finite volume schemes, hybrid high-order methods, etc.), and enable complete convergence analysis (via error estimates or compactness techniques) for a variety of models, including some encountered in real-world applications.

Various highlights:

My pages in research databases

Publications

  1. The Hybrid High-Order Method for Polytopal Meshes: Design, Analysis, and Applications [Preprint].
    Daniele Antonio Di Pietro and Jérôme Droniou.
    Modeling, Simulation and Applications, vol 19. Springer International Publishing, xxxi + 525p, 2020.
    ISBN: 978-3-030-37202-6 (Hardcover), 978-3-030-37203-3 (eBook), DOI: 10.1007/978-3-030-37203-3.
  2. The gradient discretisation method [Preprint].
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, and Raphaèle Herbin.
    Mathematics & Applications, vol 82. Springer, 511p, 2018.
    ISBN: 978-3-319-79041-1 (Softcover) 978-3-319-79042-8 (eBook), DOI: 10.1007/978-3-319-79042-8.
  1. Non-conforming Finite Elements on Polytopal Meshes [Preprint].
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, and Raphaèle Herbin.
    SEMA--SIMAI series, vol 27. Springer International Publishing, 1–35, 2021.
    ISBN: 978-3-030-69363-3, DOI: 10.1007/978-3-030-69363-3_1.
  2. Error Estimates for the Gradient Discretisation Method on Degenerate Parabolic Equations of Porous Medium Type [Preprint].
    Clément Cancès, Jérôme Droniou, Cindy Guichard, Gianmarco Manzini, Manuela Bastidas Olivares, and Iuliu Sorin Pop.
    SEMA--SIMAI series, vol 27. Springer International Publishing, 37–72, 2021.
    ISBN: 978-3-030-69363-3, DOI: 10.1007/978-3-030-69363-3_2.
  1. An exterior calculus framework for polytopal methods [Preprint].
    Francesco Bonaldi, Daniele A. Di Pietro, Jérôme Droniou, and Kaibo Hu.
    Journal of the European Mathematical Society 55p, 2024.
  2. Numerical analysis of the stochastic Stefan problem [Preprint].
    Jérôme Droniou, Muhammad Awais Khan, and Kim-Ngan Le.
    Comput. Math. Appl. 173 , 114-140, 2024
    DOI: 10.1016/j.camwa.2024.08.007.
  3. Discretisations of mixed-dimensional Thermo-Hydro-Mechanical models preserving energy estimates [Preprint].
    Jérôme Droniou, Mohamed Laaziri, and Roland Masson.
    J. Comput. Phys. 515 , Paper no. 113295, 24p, 2024
    DOI: 10.1016/j.jcp.2024.113295.
  4. Two arbitrary-order constraint-preserving schemes for the Yang–Mills equations on polyhedral meshes [Preprint].
    Jérôme Droniou and Jia Jia Qian.
    Mathematics in Engineering 6 (3), 468–493, 2024
    DOI: 10.3934/mine.2024019.
  5. The eXtended Virtual Element Method for elliptic problems with weakly singular solutions [Preprint].
    Jérôme Droniou, Gianmarco Manzini, and Liam Yemm.
    Comput. Methods Appl. Mech. Engrg. 429 , Paper No. 117129, 16p, 2024
    DOI: 10.1016/j.cma.2024.117129.
  6. Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity [Preprint].
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, and Raphaèle Herbin.
    SeMA 28p, 2024 (to appear)
    DOI: 10.1007/s40324-024-00360-w.
  7. A bubble VEM–fully discrete polytopal scheme for mixed-dimensional poromechanics with frictional contact at matrix fracture interfaces [Preprint].
    Jérôme Droniou, Guillaume Enchéry, Isabelle Faille, Ali Haidar, and Roland Masson.
    Comput. Methods Appl. Mech. Engrg. 422 , Paper no. 116838, 25p, 2024
    DOI: 10.1016/j.cma.2024.116838.
  8. A pressure-robust Discrete de Rham scheme for the Navier-Stokes equations [Preprint].
    Daniele A. Di Pietro, Jérôme Droniou, and Jia Jia Qian.
    Comput. Methods Appl. Mech. Engrg. 421 , Paper no. 116765, 21p, 2024
    DOI: 10.1016/j.cma.2024.116765.
  9. Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix–fracture interfaces [Preprint].
    Francesco Bonaldi, Jérôme Droniou, and Roland Masson.
    Math. Comp. 93 (349), 2103–2134, 2024
    DOI: 10.1090/mcom/3949.
  10. Cohomology of the discrete de Rham complex on domains of general topology [Preprint].
    Daniele A. Di Pietro, Jérôme Droniou, and Silvano Pitassi.
    Calcolo 60 (2), Paper No. 32, 25p, 2023
    DOI: 10.1007/s10092-023-00523-7.
  11. A polytopal method for the Brinkman problem robust in all regimes [Preprint].
    Daniele A. Di Pietro and Jérôme Droniou.
    Comput. Methods Appl. Mech. Engrg. 409 , Paper no. 115981, 33p, 2023
    DOI: 10.1016/j.cma.2023.115981.
  12. An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincaré inequalities, and consistency [Preprint].
    Daniele A. Di Pietro and Jérôme Droniou.
    Found. Comput. Math. 23 , 85–164, 2023
    DOI: 10.1007/s10208-021-09542-8.
  13. A hybrid high-order scheme for the stationary, incompressible magnetohydrodynamics equations [Preprint].
    Jérôme Droniou and Liam Yemm.
    IMA J. Numer. Anal. 44 (1), 262–296, 2024
    DOI: 10.1093/imanum/drad005.
  14. A polyhedral discrete de Rham numerical scheme for the Yang–Mills equations [Preprint].
    Jérôme Droniou, Todd A. Oliynyk, and Jia Jia Qian.
    J. Comput. Phys. 478 , Paper no. 111955, 26p, 2023
    DOI: 10.1016/j.jcp.2023.111955.
  15. A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem [Preprint].
    Daniele A. Di Pietro and Jérôme Droniou.
    Math. Comp. 92 , 51–77, 2023
    DOI: 10.1090/mcom/3765.
  16. Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method [Preprint].
    Daniele A. Di Pietro and Jérôme Droniou.
    M2AN Math. Model. Numer. Anal. 57 , 191–225, 2023
    DOI: 10.1051/m2an/2022067.
  17. A discrete de Rham method for the Reissner-Mindlin plate bending problem on polygonal meshes [Preprint].
    Daniele A. Di Pietro and Jérôme Droniou.
    Comput. Math. Appl. 125 , 136–149, 2022
    DOI: 10.1016/j.camwa.2022.08.041.
  18. Conditioning of a hybrid high-order scheme on meshes with small faces [Preprint].
    Santiago Badia, Jérôme Droniou, and Liam Yemm.
    J. Sci. Comput. 92 (2), Paper No. 71, 23, 2022
    DOI: 10.1007/s10915-022-01913-9.
  19. A cost-effective nonlinear extremum-preserving finite volume scheme for highly anisotropic diffusion on Cartesian grids, with application to radiation belt dynamics [Preprint].
    Nour Dahmen, Jérôme Droniou, and François Rogier.
    J. Comput. Phys. 111258, 2022
    DOI: 10.1016/j.jcp.2022.111258.
  20. Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes [Preprint].
    Lourenço Beirão da Veiga, Franco Dassi, Daniele A. Di Pietro, and Jérôme Droniou.
    Comput. Methods Appl. Mech. Engrg. 397 , Paper No. 115061, 31p, 2022
    DOI: 10.1016/j.cma.2022.115061.
  21. Design and convergence analysis of numerical methods for stochastic evolution equations with Leray–Lions operator [Preprint].
    Jérôme Droniou, Beniamin Goldys, and Kim-Ngan Le.
    IMA J. Numer. Anal. 42 (2), 1143–1179, 2022
    DOI: 10.1093/imanum/draa105.
  22. Convergence analysis of a numerical scheme for a tumour growth model [Preprint].
    Jérôme Droniou, Neela Nataraj, and Gopikrishnan C. Remesan.
    IMA J. Numer. Anal. 42 (2), 1180–1230, 2022
    DOI: 10.1093/imanum/drab016.
  23. Energy-stable discretization of two-phase flows in deformable porous media with frictional contact at matrix–fracture interfaces [Preprint].
    Francesco Bonaldi, Jérôme Droniou, Roland Masson, and Antoine Pasteau.
    J. Comput. Phys. 455 , Paper No. 110984, 2022
    DOI: 10.1016/j.jcp.2022.110984.
  24. A combined GDM–ELLAM–MMOC scheme for advection dominated PDEs [Preprint].
    Hanz Martin Cheng, Jérôme Droniou, and Kim-Ngan Le.
    Journal of Computational and Applied Mathematics 404 , 113878, 2022
    DOI: 10.1016/j.cam.2021.113878.
  25. Robust hybrid high-order method on polytopal meshes with small faces [Preprint].
    Jérôme Droniou and Liam Yemm.
    Comput. Methods Appl. Math. 22 (1), 47–71, 2022
    DOI: 10.1515/cmam-2021-0018.
  26. Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces [Preprint].
    Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou, Roland Masson, Antoine Pasteau, and Laurent Trenty.
    M2AN Math. Model. Numer. Anal. 55 (5), 1741–1777, 2021
    DOI: 10.1051/m2an/2021036.
  27. Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media [Preprint].
    Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou, and Roland Masson.
    Comput. Math. Appl. 98 , 40–68, 2021
    DOI: 10.1016/j.camwa.2021.06.017.
  28. Application of diffusion-advection equations to in-field monitoring of soil suction profiles [Preprint].
    Srikanth Venkatesan, Jérôme Droniou, Indrajit Roy, Dilan Robert, and Annan Zhou.
    Computers and Geotechnics 139 , 104329, 2021
    DOI: https://doi.org/10.1016/j.compgeo.2021.104329.
  29. Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems [Preprint].
    Daniele A. Di Pietro, Jérôme Droniou, and André Harnist.
    Calcolo 58 (2), Paper No. 19, 24p, 2021
    DOI: 10.1007/s10092-021-00410-z.
  30. Total velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure [Preprint].
    K. Brenner, R. Masson, E. H. Quenjel, and J. Droniou.
    IMA J. Numer. Anal. 42 (2), 1231–1272, 2022
    DOI: 10.1093/imanum/drab018.
  31. An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence [Preprint].
    Daniele A. Di Pietro and Jérôme Droniou.
    J. Comput. Phys. 429 , 109991, 28p, 2021
    DOI: 10.1016/j.jcp.2020.109991.
  32. Hessian discretisation method for fourth-order semi-linear elliptic equations: applications to the von K\'arm\'an and Navier-Stokes models [Preprint].
    Jérome Droniou, Neela Nataraj, and Devika Shylaja.
    Adv. Comput. Math. 47 (2), Paper No. 20, 28p, 2021
    DOI: 10.1007/s10444-020-09837-4.
  33. Numerical solution of a two dimensional tumour growth model with moving boundary [Preprint].
    Jérôme Droniou, Jennifer A. Flegg, and Gopikrishnan C. Remesan.
    J. Sci. Comput. 85 (22), Paper No. 22, 31p, 2020
    DOI: 10.1007/s10915-020-01326-6.
  34. Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra [Preprint].
    Daniele A. Di Pietro, Jérôme Droniou, and Francesca Rapetti.
    Math. Models Methods Appl. Sci. 30 (9), 1809–1855, 2020
    DOI: 10.1142/S0218202520500372.
  35. The gradient discretisation method for slow and fast diffusion porous media equations [Preprint].
    Jérôme Droniou and Kim-Ngan Le.
    SIAM J. Numer. Anal. 58 (3), 1965–1992, 2020
    DOI: 10.1137/19M1260165.
  36. An Efficient Implementation of Mass Conserving Characteristic-Based Schemes in Two and Three Dimensions [Preprint].
    Hanz Martin Cheng and Jérôme Droniou.
    SIAM J. Sci. Comput. 42 (2), A1071–A1096, 2020
    DOI: 10.1137/19M1281812.
  37. High-order mass-lumped schemes for nonlinear degenerate elliptic equations [Preprint].
    Jérôme Droniou and Robert Eymard.
    SIAM J. Numer. Anal. 58 (1), 153–188, 2020
    DOI: 10.1137/19M1244500.
  38. Limits of the Stokes and Navier–Stokes equations in a punctured periodic domain [Preprint].
    Michel Chipot, Jérôme Droniou, Gabriela Planas, James~C. Robinson, and Wei Xue.
    Analysis and Applications 18 (2), 211–235, 2020
    DOI: 10.1142/S0219530519500118.
  39. A unified analysis of elliptic problems with various boundary conditions and their approximation [Preprint].
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, and Raphalèle Herbin.
    Czechoslovak Mathematical Journal 70 (145), 339-368, 2020
    DOI: 10.21136/CMJ.2019.0312-18.
  40. The gradient discretisation method for linear advection problems [Preprint].
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, and Raphaèle Herbin.
    Comput. Methods Appl. Math. 23p, 2019
    DOI: 10.1515/cmam-2019-0060.
  41. Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling [Preprint].
    Jérôme Droniou, Matej Medla, and Karol Mikula.
    J. Comput. Phys. 398 , 108876, 2019
    DOI: 10.1016/j.jcp.2019.108876.
  42. A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device [Preprint].
    Lorenzo Botti, Daniele A. Di Pietro, and Jérôme Droniou.
    J. Comput. Phys. 376 , 786-816, 2019
    DOI: 10.1016/j.jcp.2018.10.014.
  43. An HMM–ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media [Preprint].
    Hanz Martin Cheng and Jérôme Droniou.
    J. Petrol. Science and Engineering 172 , 707–723, 2019
    DOI: 10.1016/j.petrol.2018.08.062.
  44. A mixed finite element method for a sixth-order elliptic problem [Preprint].
    Jérôme Droniou, Muhammad Ilyas, Bishnu P. Lamichhane, and Glen E. Wheeler.
    IMA J. Numer. Anal. 39 (1), 374–397, 2019
    DOI: 10.1093/imanum/drx066.
  45. Numerical analysis of a two-phase flow discrete fracture matrix model [Preprint].
    Jérôme Droniou, Julian Hennicker, and Roland Masson.
    Numer. Math. 141 (1), 21–62, 2019
    DOI: 10.1007/s00211-018-0994-y.
  46. The Hessian discretisation method for fourth order linear elliptic equations [Preprint].
    Jérôme Droniou, Bishnu P. Lamichhane, and Devika Shylaja.
    J. Sci. Comput. 78 (3), 1405–1437, 2019
    DOI: 10.1007/s10915-018-0814-7.
  47. Convergence analysis of a family of ELLAM schemes for a fully coupled model of miscible displacement in porous media [Preprint].
    Hanz Martin Cheng, Jérôme Droniou, and Kim-Ngan Le.
    Numer. Math. 141 (2), 353–397, 2019
    DOI: 10.1007/s00211-018-1002-2.
  48. Unified convergence analysis of numerical schemes for a miscible displacement problem [Preprint].
    Jérôme Droniou, Robert Eymard, Alain Prignet, and Kyle S. Talbot.
    Found. Comput. Math. 19 (2), 333-374, 2019
    DOI: 10.1007/s10208-018-9387-y.
  49. A third Strang lemma and an Aubin-Nitsche trick for schemes in fully discrete formulation [Preprint].
    Daniele A. Di Pietro and Jérôme Droniou.
    Calcolo 55 (3), Art. 40, 39p, 2018
    DOI: 10.1007/s10092-018-0282-3.
  50. A Hybrid High-Order discretisation of the Brinkman problem robust in the Darcy and Stokes limits [Preprint].
    Lorenzo Botti, Daniele A. Di Pietro, and Jérôme Droniou.
    Comput. Methods Appl. Mech. Engrg. 341 , 278–310, 2018
    DOI: 10.1016/j.cma.2018.07.004.
  51. An Eclectic View on Numerical Methods for PDEs: Presentation of the Special Issue ``Advanced Numerical Methods: Recent Developments, Analysis and Applications'' [Preprint].
    Paola F. Antonietti, Jérôme Droniou, and Robert Eymard.
    Comput. Methods Appl. Math. 18 (3), 323–325, 2018
    DOI: 10.1515/cmam-2018-0011.
  52. A Gradient Discretization Method to Analyze Numerical Schemes for Nonlinear Variational Inequalities, Application to the Seepage Problem [Preprint].
    Yahya Alnashri and Jérôme Droniou.
    SIAM J. Numer. Anal. 56 (4), 2375–2405, 2018
    DOI: 10.1137/16M1105517.
  53. An arbitrary-order scheme on generic meshes for miscible displacements in porous media [Preprint].
    Daniel Anderson and Jérôme Droniou.
    SIAM J. Sci. Comput. 40 (4), B1020–B1054, 2018
    DOI: 10.1137/17M1138807.
  54. Discontinuous skeletal gradient discretisation methods on polytopal meshes [Preprint].
    Daniele A. Di Pietro, Jérôme Droniou, and Gianmarco Manzini.
    J. Comput. Phys. 355 , 397–425, 2018
    DOI: 10.1016/j.jcp.2017.11.018.
  55. Analysis of miscible displacement through porous media with vanishing molecular diffusion and singular wells [Preprint].
    Jérôme Droniou and Kyle S. Talbot.
    Ann. Inst. H. Poincaré (C) Anal. Non Linéaire 35 (1), 1–25, 2018
    DOI: 10.1016/j.anihpc.2017.02.002.
  56. Improved $L^2$ estimate for gradient schemes and super-convergence of the TPFA finite volume scheme [Preprint].
    Jérôme Droniou and Neela Nataraj.
    IMA J. Numer. Anal. 38 (3), 1254–1293, 2018
    DOI: 10.1093/imanum/drx028.
  57. Numerical analysis for the pure Neumann control problem using the gradient discretisation method [Preprint].
    Jérome Droniou, Neela Nataraj, and Devika Shylaja.
    Comput. Methods Appl. Math. 18 (4), 609–637, 2018
    DOI: 10.1515/cmam-2017-0054.
  58. The gradient discretization method for optimal control problems, with superconvergence for nonconforming finite elements and mixed-hybrid mimetic finite differences [Preprint].
    Jérome Droniou, Neela Nataraj, and Devika Shylaja.
    SIAM J. Control Optim. 55 (6), 3640–3672, 2017
    DOI: 10.1137/17M1117768.
  59. A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes [Preprint].
    Daniele A. Di Pietro and Jérôme Droniou.
    Math. Comp. 86 (307), 2159–2191, 2017
    DOI: 10.1090/mcom/3180.
  60. $W^s,p$-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems [Preprint].
    Daniele A. Di Pietro and Jérôme Droniou.
    Math. Models Methods Appl. Sci. 27 (5), 879–908, 2017
    DOI: 10.1142/S0218202517500191.
  61. Gradient schemes: generic tools for the numerical analysis of diffusion equations [Preprint].
    Jérôme Droniou, Robert Eymard, and Raphaèle Herbin.
    M2AN Math. Model. Numer. Anal. 50 (3), 749–781, 2016
    DOI: 10.1051/m2an/2015079.
  62. Gradient schemes for the Signorini and the obstacle problems, and application to hybrid mimetic mixed methods [Preprint].
    Yahya Alnashri and Jérôme Droniou.
    Computers and Mathematics with Applications 72 , 2788-2807, 2016
    DOI: 10.1016/j.camwa.2016.10.004.
  63. Convergence in $C([0;T];L^2(\Omega))$ of weak solutions to perturbed doubly degenerate parabolic equations [Preprint].
    Jérôme Droniou, Robert Eymard, and Kyle S. Talbot.
    J. Differential Equations 260 (11), 7821–7860, 2016
    DOI: 10.1016/j.jde.2016.02.004.
  64. Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations [Preprint].
    Jérôme Droniou and Robert Eymard.
    Numer. Math. 132 (4), 721–766, 2016
    DOI: 10.1007/s00211-015-0733-6.
  65. Gradient Schemes for Stokes problem [Preprint].
    Jérôme Droniou, Robert Eymard, and Pierre Feron.
    IMA J. Numer. Anal. 36 (4), 1636–1669, 2016
    DOI: 10.1093/imanum/drv061.
  66. A discontinuous-skeletal method for advection-diffusion-reaction on general meshes [Preprint].
    Daniele A. Di Pietro, Jérôme Droniou, and Alexandre Ern.
    SIAM J. Numer. Anal. 53 (5), 2135–2157, 2015
    DOI: 10.1137/140993971.
  67. Gradient schemes for linear and non-linear elasticity equations [Preprint].
    Jérôme Droniou and Bishnu P. Lamichhane.
    Numer. Math. 129 (2), 251–277, 2015
    DOI: 10.1007/s00211-014-0636-y.
  68. On a miscible displacement model in porous media flow with measure data [Preprint].
    Jérôme Droniou and Kyle S. Talbot.
    SIAM J. Math. Anal. 46 (5), 3158–3175, 2014
    DOI: 10.1137/130949294.
  69. Finite volume schemes for diffusion equations: introduction to and review of modern methods [Preprint].
    Jérôme Droniou.
    Math. Models Methods Appl. Sci. 24 (8), 1575–1619, 2014
    DOI: 10.1142/S0218202514400041.
  70. Gradient schemes: a generic framework for the discretisation of linear, nonlinear and nonlocal elliptic and parabolic equations [Preprint].
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, and Raphaele Herbin.
    Math. Models Methods Appl. Sci. 23 (13), 2395–2432, 2013
    DOI: 10.1142/S0218202513500358.
  71. General fractal conservation laws arising from a model of detonations in gases [Preprint].
    Matthieu Alfaro and Jérôme Droniou.
    Appl. Math. Res. Express. AMRX 2012 (2), 127–151, 2012.
  72. Convergence rate of the Allen-Cahn equation to generalized motion by mean curvature [Preprint].
    Matthieu Alfaro, Jérôme Droniou, and Hiroshi Matano.
    J. Evol. Equ. 12 (2), 267–294, 2012
    DOI: 10.1007/s00028-011-0132-0.
  73. A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems [Preprint].
    Lourenco Beirão da Veiga, Jérôme Droniou, and Gianmarco Manzini.
    IMA J. Numer. Anal. 31 (4), 1357–1401, 2011
    DOI: 10.1093/imanum/drq018.
  74. Construction and convergence study of schemes preserving the elliptic local maximum principle [Preprint].
    Jérôme Droniou and Christophe Le Potier.
    SIAM J. Numer. Anal. 49 (2), 459–490, 2011
    DOI: 10.1137/090770849.
  75. Finite-volume schemes for noncoercive elliptic problems with Neumann boundary conditions [Preprint].
    Claire Chainais-Hillairet and Jérôme Droniou.
    IMA J. Numer. Anal. 31 (1), 61–85, 2011
    DOI: 10.1093/imanum/drp009.
  76. The G method for heterogeneous anisotropic diffusion on general meshes [Preprint].
    Léo Agélas, Daniele A. Di Pietro, and Jérôme Droniou.
    M2AN Math. Model. Numer. Anal. 44 (4), 597–625, 2010
    DOI: 10.1051/m2an/2010021.
  77. A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods [Preprint].
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, and Raphaèle Herbin.
    Math. Models Methods Appl. Sci. 20 (2), 265–295, 2010
    DOI: 10.1142/S0218202510004222.
  78. A numerical method for fractal conservation laws [Preprint].
    Jérôme Droniou.
    Math. Comp. 79 (269), 95–124, 2010
    DOI: 10.1090/S0025-5718-09-02293-5.
  79. Noncoercive convection-diffusion elliptic problems with Neumann boundary conditions [Preprint].
    Jérôme Droniou and Juan-Luis V\'azquez.
    Calc. Var. Partial Differential Equations 34 (4), 413–434, 2009
    DOI: 10.1007/s00526-008-0189-y.
  80. Study of the mixed finite volume method for Stokes and Navier-Stokes equations [Preprint].
    Jérôme Droniou and Robert Eymard.
    Numer. Methods Partial Differential Equations 25 (1), 137–171, 2009
    DOI: 10.1002/num.20333.
  81. Convergence analysis of a mixed finite volume scheme for an elliptic-parabolic system modeling miscible fluid flows in porous media [Preprint].
    Claire Chainais-Hillairet and Jérôme Droniou.
    SIAM J. Numer. Anal. 45 (5), 2228–2258 (electronic), 2007
    DOI: 10.1137/060657236.
  82. Equivalence between entropy and renormalized solutions for parabolic equations with smooth measure data [Preprint].
    Jérôme Droniou and Alain Prignet.
    NoDEA Nonlinear Differential Equations Appl. 14 (1-2), 181–205, 2007
    DOI: 10.1007/s00030-007-5018-z.
  83. Occurrence and non-appearance of shocks in fractal Burgers equations [Preprint].
    Nathaël Alibaud, Jérôme Droniou, and Julien Vovelle.
    J. Hyperbolic Differ. Equ. 4 (3), 479–499, 2007
    DOI: 10.1142/S0219891607001227.
  84. Finite volume schemes for fully non-linear elliptic equations in divergence form [Preprint].
    Jérôme Droniou.
    M2AN Math. Model. Numer. Anal. 40 (6), 1069–1100, 2006
    DOI: 10.1051/m2an:2007001.
  85. Fractal first-order partial differential equations [Preprint].
    Jérôme Droniou and Cyril Imbert.
    Arch. Ration. Mech. Anal. 182 (2), 299–331, 2006
    DOI: 10.1007/s00205-006-0429-2.
  86. A mixed finite volume scheme for anisotropic diffusion problems on any grid [Preprint].
    Jérôme Droniou and Robert Eymard.
    Numer. Math. 105 (1), 35–71, 2006
    DOI: 10.1007/s00211-006-0034-1.
  87. An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions [Preprint].
    Jérôme Droniou, Cyril Imbert, and Julien Vovelle.
    Ann. Inst. H. Poincaré (C) Anal. Non Linéaire 21 (5), 689–714, 2004
    DOI: 10.1016/j.anihpc.2003.11.001.
  88. A finite volume scheme for a noncoercive elliptic equation with measure data [Preprint].
    Jérôme Droniou, Thierry Gallouët, and Raphaèle Herbin.
    SIAM J. Numer. Anal. 41 (6), 1997–2031 (electronic), 2003
    DOI: 10.1137/S0036142902405205.
  89. Global solution and smoothing effect for a non-local regularization of a hyperbolic equation [Preprint].
    Jérôme Droniou, Thierry Gallouët, and Julien Vovelle.
    J. Evol. Equ. 3 (3), 499–521, 2003
    DOI: 10.1007/s00028-003-0503-1.
  90. Vanishing non-local regularization of a scalar conservation law [Preprint].
    Jérôme Droniou.
    Electron. J. Differential Equations No. 117, 20 pp. (electronic), 2003.
  91. Convergence of a finite-volume mixed finite-element method for an elliptic-hyperbolic system [Preprint].
    Jérôme Droniou, Robert Eymard, Danielle Hilhorst, and Xue Dong Zhou.
    IMA J. Numer. Anal. 23 (3), 507–538, 2003
    DOI: 10.1093/imanum/23.3.507.
  92. Error estimates for the convergence of a finite volume discretization of convection-diffusion equations [Preprint].
    Jérôme Droniou.
    J. Numer. Math. 11 (1), 1–32, 2003
    DOI: 10.1163/156939503322004873.
  93. Parabolic capacity and soft measures for nonlinear equations [Preprint].
    Jérôme Droniou, Alessio Porretta, and Alain Prignet.
    Potential Anal. 19 (2), 99–161, 2003
    DOI: 10.1023/A:1023248531928.
  94. Global and local estimates for nonlinear noncoercive elliptic equations with measure data [Preprint].
    Jérôme Droniou.
    Comm. Partial Differential Equations 28 (1-2), 129–153, 2003
    DOI: 10.1081/PDE-120019377.
  95. A density result in Sobolev spaces [Preprint].
    Jérôme Droniou.
    J. Math. Pures Appl. 81 (7), 697–714, 2002
    DOI: 10.1016/S0021-7824(01)01241-7.
  96. Finite volume methods for convection-diffusion equations with right-hand side in $H^-1$ [Preprint].
    Jérôme Droniou and Thierry Gallouët.
    M2AN Math. Model. Numer. Anal. 36 (4), 705–724, 2002
    DOI: 10.1051/m2an:2002031.
  97. Non-coercive linear elliptic problems [Preprint].
    Jérôme Droniou.
    Potential Anal. 17 (2), 181–203, 2002
    DOI: 10.1023/A:1015709329011.
  98. A uniqueness result for quasilinear elliptic equations with measures as data [Preprint].
    Jérôme Droniou and Thierry Gallouët.
    Rend. Mat. Appl. (Ser. VII) 21 (1-4), 57–86, 2001.
  99. Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method [Preprint].
    Jérôme Droniou.
    Adv. Differential Equations 5 (10-12), 1341–1396, 2000.
  100. Optimal pointwise control of semilinear parabolic equations [Preprint].
    Jérôme Droniou and Jean-Pierre Raymond.
    Nonlinear Anal. 39 (2, Ser. A: Theory Methods), 135–156, 2000
    DOI: 10.1016/S0362-546X(98)00170-9.
  1. Thermodynamically Consistent discretisation of a Thermo-Hydro-Mechanical model [Preprint].
    Jérôme Droniou, Mohamed Laaziri, and Roland Masson.
    Finite volumes for complex applications X, Springer Proc. Math. Stat. 432, 265-273, 2023.
  2. Two-Phase Darcy Flows in Fractured and Deformable Porous Media, Convergence Analysis and Iterative Coupling .
    Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou, and Roland Masson.
    ECMOR XVII, 2020, 1-20, 2020
    DOI: 10.3997/2214-4609.202035013.
  3. Interplay between diffusion anisotropy and mesh skewness in Hybrid High-Order schemes [Preprint].
    Jérôme Droniou.
    Finite volumes for complex applications IX–-methods, theoretical aspects, examples, Springer Proc. Math. Stat. 323, 3-23, 2020.
  4. The gradient discretisation method for two-phase discrete fracture matrix models in deformable porous media [Preprint].
    Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou, and Roland Masson.
    Finite volumes for complex applications IX, Springer Proc. Math. Stat. 8p, 2020.
  5. An introduction to the gradient discretisation method .
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, and Raphaèle Herbin.
    Numerical Mathematics and Advanced Applications ENUMATH 2017, Lecture Notes in Computational Science and Engineering 451–459, 2019
    DOI: 10.1007/978-3-319-96415-7_40.
  6. The asymmetric gradient discretisation method [Preprint].
    J. Droniou and R. Eymard.
    Finite volumes for complex applications VIII–-methods and theoretical aspects, Springer Proc. Math. Stat. 199, 311–319, 2017.
  7. Benchmark: two hybrid mimetic mixed schemes for the lid-driven cavity [Preprint].
    Jérôme Droniou and Robert Eymard.
    Finite volumes for complex applications VIII–-methods and theoretical aspects, Springer Proc. Math. Stat. 199, 107–124, 2017.
  8. An error estimate for the approximation of linear parabolic equations by the gradient discretization method [Preprint].
    J. Droniou, R. Eymard, T. Gallouët, C. Guichard, and R. Herbin.
    Finite volumes for complex applications VIII–-methods and theoretical aspects, Springer Proc. Math. Stat. 199, 371–379, 2017.
  9. Combining the hybrid mimetic mixed method and the Eulerian Lagrangian localised adjoint method for approximating miscible flows in porous media [Preprint].
    Hanz Martin Cheng and Jérôme Droniou.
    Finite volumes for complex applications VIII–-hyperbolic, elliptic and parabolic problems, Springer Proc. Math. Stat. 200, 367–376, 2017.
  10. Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model [Preprint].
    J. Droniou, J. Hennicker, and R. Masson.
    Finite volumes for complex applications VIII–-methods and theoretical aspects, Springer Proc. Math. Stat. 199, 275–283, 2017.
  11. Introduction to discrete functional analysis techniques for the numerical study of diffusion equations with irregular data [Preprint].
    Jérôme Droniou.
    Proceedings of the 17th Biennial Computational Techniques and Applications Conference (CTAC-2014, Canberra), ANZIAM J. 56, C101-C127, 2015
    DOI: http://dx.doi.org/10.21914/anziamj.v56i0.9365.
  12. Uniform-in-time convergence of numerical schemes for Richards' and Stefan's models [Preprint].
    Jérôme Droniou, Robert Eymard, and Cindy Guichard.
    Finite volumes for complex applications. VII. Methods and theoretical aspects (Berlin, 2014), Springer Proc. Math. Stat. 77, 247–254, 2014
    DOI: 10.1007/978-3-319-05684-5_23.
  13. A uniformly converging scheme for fractal conservation laws [Preprint].
    Jérôme Droniou and Espen R. Jakobsen.
    Finite volumes for complex applications. VII. Methods and theoretical aspects (Berlin, 2014), Springer Proc. Math. Stat. 77, 237–245, 2014
    DOI: 10.1007/978-3-319-05684-5_22.
  14. Gradient schemes for an obstacle problem [Preprint].
    Yahya Alnashri and Jérôme Droniou.
    Finite volumes for complex applications. VII. Methods and theoretical aspects (Berlin, 2014), Springer Proc. Math. Stat. 77, 67–75, 2014
    DOI: 10.1007/978-3-319-05684-5_5.
  15. Remarks on discretizations of convection terms in hybrid mimetic mixed methods [Preprint].
    Jérôme Droniou.
    , 5 (3), 545–563, 2010
    DOI: 10.3934/nhm.2010.5.545.
  16. Benchmark on Anisotropic Problems – Use of the mixed finite volume method [Preprint].
    Claire Chainais-Hillairet, Jérôme Droniou, and Robert Eymard.
    Finite volumes for complex applications V (Aussois, 2008), 751–760, 2008.
  17. A recipe to couple two finite volume schemes for elliptic problems [Preprint].
    Jérôme Droniou.
    Finite volumes for complex applications V (Aussois, 2008), 69–86, 2008.
  18. Fractal conservation laws: global smooth solutions and vanishing regularization [Preprint].
    Jérôme Droniou.
    Fifth European Conference on Elliptic and Parabolic Problems: A special tribute to the work of Haim Brezis (Gaeta 2004), Progr. Nonlinear Differential Equations Appl. 63, 235–242, 2005
    DOI: 10.1007/3-7643-7384-9_24.
  19. A finite volume scheme for noncoercive Dirichlet problems with right-hand sides in $H^-1$ [Preprint].
    Jérôme Droniou and Thierry Gallouët.
    Finite volumes for complex applications, III (Porquerolles, 2002), 181–188, 2002.
  20. Contrôle de l'architecture et des représentations internes dans les réseaux de neurones multicouches, .
    Jérôme Droniou, André Elisseeff, Hélène Paugam-Moisy, and Olivier Teytaud.
    Actes de la Conférence sur l'Apprentissage CAP'99 (Palaiseau, 1999), 185–194, 1999.
  1. A discrete trace theory for non-conforming polytopal hybrid discretisation methods [Preprint].
    Santiago Badia, Jérôme Droniou, and Jai Tushar.
    34p, 2024.
  2. Analysis of a VEM–fully discrete polytopal scheme with bubble stabilisation for contact mechanics with Tresca friction [Preprint].
    Jérôme Droniou, Ali Haidar, and Roland Masson.
    31p, 2024.
  3. A polytopal discrete de Rham complex on manifolds, with application to the Maxwell equations [Preprint].
    Jérôme Droniou, Marien Hanot, and Todd Oliynyk.
    33p, 2024.

Theses

Presentations

  • Design and analysis of an extended virtual element method [slides].
    CTAC 2024 (regular presentation), Melbourne, Australia, 21 November.
  • A complete theory of discrete trace and lifting for hybrid polytopal methods [slides].
    Seminaire Laboratoire Jacques-Louis Lions, Paris, France, 25 October.
  • Bubble-stabilised polytopal scheme for flows in fractured media with frictional contact [slides].
    WCCM-PANCAM 24 (regular presentation), Vancouver, Canada, 23 July.
  • Analysis approaches for polytopal schemes – the linear and nonlinear cases [slides].
    NEMESIS Kick-off workshop (keynote), Montpellier, France, 19 June.
  • The Exterior Calculus Discrete De Rham complex [slides].
    New Trends in the Numerical Analysis of PDE (keynote), Lille, France, 11 June.
  • A bubble-enriched polytopal method for contact mechanics [slides].
    Seminaire ACSIOM, IMAG, Montpellier, France, 2 April.
  • The discrete de Rham complex, and its application to the Navier–Stokes equations [slides].
    PAMIR (Point values, Averages and Moments and their Inter-Relation) workshop (keynote), Cambridge, UK, 8 March.
  • Arbitrary-order polytopal schemes for the Yang–Mills equations [slides].
    Seminaire NAGANA, Montpellier, France, 12 September.
  • A polytopal exterior calculus framework [slides].
    ICIAM 2023 (regular presentation), Tokyo, Japan (hybrid), 23 August.
  • Serendipity discrete de Rham method [slides].
    ICOSAHOM 2023 (regular presentation), Seoul, South Korea, 16 August.
  • Introduction to the Discrete De Rham complex [slides].
    Seminar of the Mathematical Institute, Oxford, UK, 13 October.
  • Pressure-Robust Discrete De Rham and Virtual Element Schemes for the Stokes Problem [slides].
    SIAM Annual Meeting (regular presentation), Pittsburg, USA (hybrid), 11--15 July.
  • Next generation methods for the simulation of geophysical flows (and more...) [slides].
    Mathematica Solis et Terrae conference (keynote), ANU, Canberra, 11--12 April.
  • An arbitrary-order robust polygonal scheme for the Reissner-Mindlin plate problem [slides].
    AustMS annual meeting (regular presentation), Online, 7 December.
  • Convergence and error estimates of numerical schemes for the porous medium equation [slides].
    ANZIAM annual meeting (regular presentation), Online, 4 February.
  • A discrete exact grad-curl-div complex on generic polyhedral meshes Part II: Analytical properties [slides].
    16th U.S. National Congress on Computational Mechanics (regular presentation), Online, 26 July.
    (Part I is available Daniele Di Pietro's homepage)
  • Numerical analysis of two-phase flows models with mechanical deformation in fracture porous media [slides].
    AustMS annual meeting (regular presentation), UNE (Armidale, Australia), 10 December.
  • Polynomial de Rham sequences of arbitrary degree on polyhedral meshes [slides].
    Seminar, Marseille, France, 8 December.
  • High-order methods for linear and non-linear elliptic equations [slides].
    Algoritmy 2020 (keynote), Podbanske (Slovakia), 10-15 September.
  • Interplay between diffusion anisotropy and mesh skewness in Hybrid High-Order schemes [slides].
    FVCA9 (keynote), Bergen (Norway), 15-19 June.
  • A fully discrete exact de Rham sequence, with application to magnetostatics [slides].
    CTAC (regular presentation), UNSW (Sydney, Australia), 30 August - 2 September.
  • B-char: an efficient (and feasible!) approach for mass-conserving characteristic schemes in 2D and 3D [slides].
    MWNDEA (regular presentation), Monash (Melbourne, Australia), 10-14 February.

Teaching (last four years)

  • Partial Differential Equations (3rd year undergraduate): lectures (18h).
  • Advanced numerical analysis of partial differential equations (Master): lectures (18h), applied class (6h).
  • Advanced engineering mathematics (2nd year undergraduate (Engineering)): lectures (24h) and coordination.
  • Real Analysis (2nd and 3rd year undergraduate): lectures (36h) and coordination.
  • Partial Differential Equations (3rd year undergraduate): lectures (18h) and applied class (17h).
  • Advanced numerical analysis of partial differential equations (Master): lectures (18h), applied class (6h) and coordination.
  • Real Analysis (2nd and 3rd year undergraduate): lectures (36h), applied class (17h) and coordination.
  • Partial Differential Equations (3rd year undergraduate): lectures (18h).
  • Real Analysis (2nd and 3rd year undergraduate): lectures (36h), applied class (17h) and coordination.
  • Numerical analysis and control of differential equations (Master): lectures (18h), applied class (6h) and coordination.

Some lecture notes

  • Quelques Résultats sur les Espaces de Sobolev (85p), J. Droniou , Polycopié de l'Ecole Doctorale de Maths-Info de Marseille, available on HAL (in French).
  • Intégration et Espaces de Sobolev à Valeurs Vectorielles (71p), J. Droniou, Polycopié de l'Ecole Doctorale de Maths-Info de Marseille, available on HAL (in French).
  • Degrés topologiques et applications (56p), J. Droniou, pdf here (in French).
  • A beginner's course in finite volume approximation of scalar conservation laws (39p), J. Droniou, Pamplona - Pau - Toulouse - Zaragoza summer school on nonlinear conservation laws, Jaca 11-13/09/2008. pdf of the lecture notes and movies available here.
Updated 21/11/2024