Jerome Droniou

Professor in Mathematics at Monash university (Melbourne, Australia)


Address: School of Mathematics,
Monash University,
Clayton, VIC 3800,
AUSTRALIA
Phone: (+61) 3 9905 4489
Office: Room 306, 3th floor, 9 Rainforest Walk (Building 28), Clayton campus
Email: jerome.droniou*at*monash.edu

Roles

Resume in pdf


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.
    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.
    Preprint
  2. The gradient discretisation method.
    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.
    Preprint
  1. Non-conforming finite elements on polytopal meshes.
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, and Raphaèle Herbin.
    , vol . SEMA-SIMAI, 1-27, 2020 (to appear)..
    Preprint
  2. Error estimates for the gradient discretisation method on degenerate parabolic equations of porous medium type.
    Clément Cancès, Jérôme Droniou, Cindy Guichard, Gianmarco Manzini, Manuela Bastisdas, and Iuliu Sorin Pop.
    , vol . SEMA-SIMAI, 1-35, 2020 (to appear)..
    Preprint
  1. Improved error estimates for Hybrid High-Order discretizations of Leray–Lions problems.
    Daniele A. Di Pietro, Jérôme Droniou, and André Harnist.
    Calcolo 58 (19), 24p, 2021, DOI: 10.1007/s10092-021-00410-z.
    Preprint
  2. Total-velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure.
    Konstantin Brenner, Jérôme Droniou, Roland Masson, and El Houssaine Quenjel.
    IMA J. Numer. Anal. 33p, 2021 (to appear).
    Preprint
  3. An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence.
    Daniele A. Di Pietro and Jérôme Droniou.
    J. Comput. Phys. 109991, 2021, DOI: 10.1016/j.jcp.2020.109991.
    Preprint
  4. Convergence analysis of a numerical scheme for a tumour growth model.
    Jérôme Droniou, Neela Nataraj, and Gopikrishnan C. Remesan.
    IMA J. Numer. Anal. 49p, 2021 (to appear).
    Preprint
  5. Hessian discretisation method for fourth order semi-linear elliptic equations: applications to the von K\'arm\'an and Navier–Stokes models.
    Jérome Droniou, Neela Nataraj, and Devika Shylaja.
    Adv. Comput. Math. 47 (20), 27p, 2021 (to appear), DOI: 10.1007/s10444-020-09837-4.
    Preprint
  6. Design and convergence analysis of numerical methods for stochastic evolution equations with Leray–Lions operator.
    Jérôme Droniou, Beniamin Goldys, and Kim-Ngan Le.
    IMA J. Numer. Anal. 31p, 2021 (to appear).
    Preprint
  7. Numerical solution of a two dimensional tumour growth model with moving boundary.
    Jérôme Droniou, Jennifer A. Flegg, and Gopikrishnan C. Remesan.
    J. Sci. Comput. 85 (22), 31p, 2020 (to appear), DOI: 10.1007/s10915-020-01326-6.
    Preprint
  8. Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra.
    Daniele A. Di Pietro, Jérôme Droniou, and Francesca Rapetti.
    Math. Models Methods Appl. Sci. 30 (9), 1809–1855, 2020, DOI: 10.1142/S0218202520500372.
    Preprint
  9. The gradient discretisation method for slow and fast diffusion porous media equations.
    Jérôme Droniou and Kim-Ngan Le.
    SIAM J. Numer. Anal. 58 (3), 1965–1992, 2020, DOI: 10.1137/19M1260165.
    Preprint
  10. An Efficient Implementation of Mass Conserving Characteristic-Based Schemes in Two and Three Dimensions.
    Hanz Martin Cheng and Jérôme Droniou.
    SIAM J. Sci. Comput. 42 (2), A1071–A1096, 2020, DOI: 10.1137/19M1281812.
    Preprint
  11. High-order mass-lumped schemes for nonlinear degenerate elliptic equations.
    Jérôme Droniou and Robert Eymard.
    SIAM J. Numer. Anal. 58 (1), 153–188, 2020, DOI: 10.1137/19M1244500.
    Preprint
  12. Limits of the Stokes and Navier–Stokes equations in a punctured periodic domain.
    Michel Chipot, Jérôme Droniou, Gabriela Planas, James~C. Robinson, and Wei Xue.
    Analysis and Applications 18 (2), 211–235, 2020, DOI: 10.1142/S0219530519500118.
    Preprint
  13. A unified analysis of elliptic problems with various boundary conditions and their approximation.
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, and Raphalèle Herbin.
    Czechoslovak Mathematical Journal 70 (145), 339-368, 2020, DOI: 10.21136/CMJ.2019.0312-18.
    Preprint
  14. The gradient discretisation method for linear advection problems.
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, and Raphaèle Herbin.
    Comput. Methods Appl. Math. 23p, 2019, DOI: 10.1515/cmam-2019-0060.
    Preprint
  15. Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling.
    Jérôme Droniou, Matej Medla, and Karol Mikula.
    J. Comput. Phys. 398 , 108876, 2019, DOI: 10.1016/j.jcp.2019.108876.
    Preprint
  16. A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device.
    Lorenzo Botti, Daniele A. Di Pietro, and Jérôme Droniou.
    J. Comput. Phys. 376 , 786-816, 2019, DOI: 10.1016/j.jcp.2018.10.014.
    Preprint
  17. An HMM–ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media.
    Hanz Martin Cheng and Jérôme Droniou.
    J. Petrol. Science and Engineering 172 , 707–723, 2019, DOI: 10.1016/j.petrol.2018.08.062.
    Preprint
  18. A mixed finite element method for a sixth-order elliptic problem.
    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.
    Preprint
  19. Numerical analysis of a two-phase flow discrete fracture matrix model.
    Jérôme Droniou, Julian Hennicker, and Roland Masson.
    Numer. Math. 141 (1), 21–62, 2019, DOI: 10.1007/s00211-018-0994-y.
    Preprint
  20. The Hessian discretisation method for fourth order linear elliptic equations.
    Jérôme Droniou, Bishnu P. Lamichhane, and Devika Shylaja.
    J. Sci. Comput. 78 (3), 1405–1437, 2019, DOI: 10.1007/s10915-018-0814-7.
    Preprint
  21. Convergence analysis of a family of ELLAM schemes for a fully coupled model of miscible displacement in porous media.
    Hanz Martin Cheng, Jérôme Droniou, and Kim-Ngan Le.
    Numer. Math. 141 (2), 353–397, 2019, DOI: 10.1007/s00211-018-1002-2.
    Preprint
  22. Unified convergence analysis of numerical schemes for a miscible displacement problem.
    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.
    Preprint
  23. A third Strang lemma and an Aubin-Nitsche trick for schemes in fully discrete formulation.
    Daniele A. Di Pietro and Jérôme Droniou.
    Calcolo 55 (3), Art. 40, 39p, 2018, DOI: 10.1007/s10092-018-0282-3.
    Preprint
  24. A Hybrid High-Order discretisation of the Brinkman problem robust in the Darcy and Stokes limits.
    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.
    Preprint
  25. An Eclectic View on Numerical Methods for PDEs: Presentation of the Special Issue ``Advanced Numerical Methods: Recent Developments, Analysis and Applications''.
    Paola F. Antonietti, Jérôme Droniou, and Robert Eymard.
    Comput. Methods Appl. Math. 18 (3), 323–325, 2018, DOI: 10.1515/cmam-2018-0011.
    Preprint
  26. A Gradient Discretization Method to Analyze Numerical Schemes for Nonlinear Variational Inequalities, Application to the Seepage Problem.
    Yahya Alnashri and Jérôme Droniou.
    SIAM J. Numer. Anal. 56 (4), 2375–2405, 2018, DOI: 10.1137/16M1105517.
    Preprint
  27. An arbitrary-order scheme on generic meshes for miscible displacements in porous media.
    Daniel Anderson and Jérôme Droniou.
    SIAM J. Sci. Comput. 40 (4), B1020–B1054, 2018, DOI: 10.1137/17M1138807.
    Preprint
  28. Discontinuous skeletal gradient discretisation methods on polytopal meshes.
    Daniele A. Di Pietro, Jérôme Droniou, and Gianmarco Manzini.
    J. Comput. Phys. 355 , 397–425, 2018, DOI: 10.1016/j.jcp.2017.11.018.
    Preprint
  29. Analysis of miscible displacement through porous media with vanishing molecular diffusion and singular wells.
    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.
    Preprint
  30. Improved $L^2$ estimate for gradient schemes and super-convergence of the TPFA finite volume scheme.
    Jérôme Droniou and Neela Nataraj.
    IMA J. Numer. Anal. 38 (3), 1254–1293, 2018, DOI: 10.1093/imanum/drx028.
    Preprint
  31. Numerical analysis for the pure Neumann control problem using the gradient discretisation method.
    Jérome Droniou, Neela Nataraj, and Devika Shylaja.
    Comput. Methods Appl. Math. 18 (4), 609–637, 2018, DOI: 10.1515/cmam-2017-0054.
    Preprint
  32. The gradient discretization method for optimal control problems, with superconvergence for nonconforming finite elements and mixed-hybrid mimetic finite differences.
    Jérome Droniou, Neela Nataraj, and Devika Shylaja.
    SIAM J. Control Optim. 55 (6), 3640–3672, 2017, DOI: 10.1137/17M1117768.
    Preprint
  33. A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes.
    Daniele A. Di Pietro and Jérôme Droniou.
    Math. Comp. 86 (307), 2159–2191, 2017, DOI: 10.1090/mcom/3180.
    Preprint
  34. $W^s,p$-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems.
    Daniele A. Di Pietro and Jérôme Droniou.
    Math. Models Methods Appl. Sci. 27 (5), 879–908, 2017, DOI: 10.1142/S0218202517500191.
    Preprint
  35. Gradient schemes: generic tools for the numerical analysis of diffusion equations.
    Jérôme Droniou, Robert Eymard, and Raphaèle Herbin.
    M2AN Math. Model. Numer. Anal. 50 (3), 749–781, 2016, DOI: 10.1051/m2an/2015079.
    Preprint
  36. Gradient schemes for the Signorini and the obstacle problems, and application to hybrid mimetic mixed methods.
    Yahya Alnashri and Jérôme Droniou.
    Computers and Mathematics with Applications 72 , 2788-2807, 2016, DOI: 10.1016/j.camwa.2016.10.004.
    Preprint
  37. Convergence in $C([0;T];L^2(\Omega))$ of weak solutions to perturbed doubly degenerate parabolic equations.
    Jérôme Droniou, Robert Eymard, and Kyle S. Talbot.
    J. Differential Equations 260 (11), 7821–7860, 2016, DOI: 10.1016/j.jde.2016.02.004.
    Preprint
  38. Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations.
    Jérôme Droniou and Robert Eymard.
    Numer. Math. 132 (4), 721–766, 2016, DOI: 10.1007/s00211-015-0733-6.
    Preprint
  39. Gradient Schemes for Stokes problem.
    Jérôme Droniou, Robert Eymard, and Pierre Feron.
    IMA J. Numer. Anal. 36 (4), 1636–1669, 2016, DOI: 10.1093/imanum/drv061.
    Preprint
  40. A discontinuous-skeletal method for advection-diffusion-reaction on general meshes.
    Daniele A. Di Pietro, Jérôme Droniou, and Alexandre Ern.
    SIAM J. Numer. Anal. 53 (5), 2135–2157, 2015, DOI: 10.1137/140993971.
    Preprint
  41. Gradient schemes for linear and non-linear elasticity equations.
    Jérôme Droniou and Bishnu P. Lamichhane.
    Numer. Math. 129 (2), 251–277, 2015, DOI: 10.1007/s00211-014-0636-y.
    Preprint
  42. On a miscible displacement model in porous media flow with measure data.
    Jérôme Droniou and Kyle S. Talbot.
    SIAM J. Math. Anal. 46 (5), 3158–3175, 2014, DOI: 10.1137/130949294.
    Preprint
  43. Finite volume schemes for diffusion equations: introduction to and review of modern methods.
    Jérôme Droniou.
    Math. Models Methods Appl. Sci. 24 (8), 1575–1619, 2014, DOI: 10.1142/S0218202514400041.
    Preprint
  44. Gradient schemes: a generic framework for the discretisation of linear, nonlinear and nonlocal elliptic and parabolic equations.
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, and Raphaele Herbin.
    Math. Models Methods Appl. Sci. 23 (13), 2395–2432, 2013, DOI: 10.1142/S0218202513500358.
    Preprint
  45. General fractal conservation laws arising from a model of detonations in gases.
    Matthieu Alfaro and Jérôme Droniou.
    Appl. Math. Res. Express. AMRX 2012 (2), 127–151, 2012.
    Preprint
  46. Convergence rate of the Allen-Cahn equation to generalized motion by mean curvature.
    Matthieu Alfaro, Jérôme Droniou, and Hiroshi Matano.
    J. Evol. Equ. 12 (2), 267–294, 2012, DOI: 10.1007/s00028-011-0132-0.
    Preprint
  47. A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems.
    Lourenco Beir\~ao da Veiga, Jérôme Droniou, and Gianmarco Manzini.
    IMA J. Numer. Anal. 31 (4), 1357–1401, 2011, DOI: 10.1093/imanum/drq018.
    Preprint
  48. Construction and convergence study of schemes preserving the elliptic local maximum principle.
    Jérôme Droniou and Christophe Le Potier.
    SIAM J. Numer. Anal. 49 (2), 459–490, 2011, DOI: 10.1137/090770849.
    Preprint
  49. Finite-volume schemes for noncoercive elliptic problems with Neumann boundary conditions.
    Claire Chainais-Hillairet and Jérôme Droniou.
    IMA J. Numer. Anal. 31 (1), 61–85, 2011, DOI: 10.1093/imanum/drp009.
    Preprint
  50. The G method for heterogeneous anisotropic diffusion on general meshes.
    Léo Agélas, Daniele A. Di Pietro, and Jérôme Droniou.
    M2AN Math. Model. Numer. Anal. 44 (4), 597–625, 2010, DOI: 10.1051/m2an/2010021.
    Preprint
  51. A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods.
    Jérôme Droniou, Robert Eymard, Thierry Gallouët, and Raphaèle Herbin.
    Math. Models Methods Appl. Sci. 20 (2), 265–295, 2010, DOI: 10.1142/S0218202510004222.
    Preprint
  52. A numerical method for fractal conservation laws.
    Jérôme Droniou.
    Math. Comp. 79 (269), 95–124, 2010, DOI: 10.1090/S0025-5718-09-02293-5.
    Preprint
  53. Noncoercive convection-diffusion elliptic problems with Neumann boundary conditions.
    Jérôme Droniou and Juan-Luis V\'azquez.
    Calc. Var. Partial Differential Equations 34 (4), 413–434, 2009, DOI: 10.1007/s00526-008-0189-y.
    Preprint
  54. Study of the mixed finite volume method for Stokes and Navier-Stokes equations.
    Jérôme Droniou and Robert Eymard.
    Numer. Methods Partial Differential Equations 25 (1), 137–171, 2009, DOI: 10.1002/num.20333.
    Preprint
  55. Convergence analysis of a mixed finite volume scheme for an elliptic-parabolic system modeling miscible fluid flows in porous media.
    Claire Chainais-Hillairet and Jérôme Droniou.
    SIAM J. Numer. Anal. 45 (5), 2228–2258 (electronic), 2007, DOI: 10.1137/060657236.
    Preprint
  56. Equivalence between entropy and renormalized solutions for parabolic equations with smooth measure data.
    Jérôme Droniou and Alain Prignet.
    NoDEA Nonlinear Differential Equations Appl. 14 (1-2), 181–205, 2007, DOI: 10.1007/s00030-007-5018-z.
    Preprint
  57. Occurrence and non-appearance of shocks in fractal Burgers equations.
    Nathaël Alibaud, Jérôme Droniou, and Julien Vovelle.
    J. Hyperbolic Differ. Equ. 4 (3), 479–499, 2007, DOI: 10.1142/S0219891607001227.
    Preprint
  58. Finite volume schemes for fully non-linear elliptic equations in divergence form.
    Jérôme Droniou.
    M2AN Math. Model. Numer. Anal. 40 (6), 1069–1100, 2006, DOI: 10.1051/m2an:2007001.
    Preprint
  59. Fractal first-order partial differential equations.
    Jérôme Droniou and Cyril Imbert.
    Arch. Ration. Mech. Anal. 182 (2), 299–331, 2006, DOI: 10.1007/s00205-006-0429-2.
    Preprint
  60. A mixed finite volume scheme for anisotropic diffusion problems on any grid.
    Jérôme Droniou and Robert Eymard.
    Numer. Math. 105 (1), 35–71, 2006, DOI: 10.1007/s00211-006-0034-1.
    Preprint
  61. An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions.
    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.
    Preprint
  62. A finite volume scheme for a noncoercive elliptic equation with measure data.
    Jérôme Droniou, Thierry Gallouët, and Raphaèle Herbin.
    SIAM J. Numer. Anal. 41 (6), 1997–2031 (electronic), 2003, DOI: 10.1137/S0036142902405205.
    Preprint
  63. Global solution and smoothing effect for a non-local regularization of a hyperbolic equation.
    Jérôme Droniou, Thierry Gallouët, and Julien Vovelle.
    J. Evol. Equ. 3 (3), 499–521, 2003, DOI: 10.1007/s00028-003-0503-1.
    Preprint
  64. Vanishing non-local regularization of a scalar conservation law.
    Jérôme Droniou.
    Electron. J. Differential Equations No. 117, 20 pp. (electronic), 2003.
    Preprint
  65. Convergence of a finite-volume mixed finite-element method for an elliptic-hyperbolic system.
    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.
    Preprint
  66. Error estimates for the convergence of a finite volume discretization of convection-diffusion equations.
    Jérôme Droniou.
    J. Numer. Math. 11 (1), 1–32, 2003, DOI: 10.1163/156939503322004873.
    Preprint
  67. Parabolic capacity and soft measures for nonlinear equations.
    Jérôme Droniou, Alessio Porretta, and Alain Prignet.
    Potential Anal. 19 (2), 99–161, 2003, DOI: 10.1023/A:1023248531928.
    Preprint
  68. Global and local estimates for nonlinear noncoercive elliptic equations with measure data.
    Jérôme Droniou.
    Comm. Partial Differential Equations 28 (1-2), 129–153, 2003, DOI: 10.1081/PDE-120019377.
    Preprint
  69. A density result in Sobolev spaces.
    Jérôme Droniou.
    J. Math. Pures Appl. 81 (7), 697–714, 2002, DOI: 10.1016/S0021-7824(01)01241-7.
    Preprint
  70. Finite volume methods for convection-diffusion equations with right-hand side in $H^-1$.
    Jérôme Droniou and Thierry Gallouët.
    M2AN Math. Model. Numer. Anal. 36 (4), 705–724, 2002, DOI: 10.1051/m2an:2002031.
    Preprint
  71. Non-coercive linear elliptic problems.
    Jérôme Droniou.
    Potential Anal. 17 (2), 181–203, 2002, DOI: 10.1023/A:1015709329011.
    Preprint
  72. A uniqueness result for quasilinear elliptic equations with measures as data.
    Jérôme Droniou and Thierry Gallouët.
    Rend. Mat. Appl. (Ser. VII) 21 (1-4), 57–86, 2001.
    Preprint
  73. Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method.
    Jérôme Droniou.
    Adv. Differential Equations 5 (10-12), 1341–1396, 2000.
    Preprint
  74. Optimal pointwise control of semilinear parabolic equations.
    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.
    Preprint
  1. 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.
  2. Interplay between diffusion anisotropy and mesh skewness in Hybrid High-Order schemes.
    Jérôme Droniou.
    Finite volumes for complex applications IX–-methods, theoretical aspects, examples, Springer Proc. Math. Stat. 323, 3-23, 2020.
    Preprint
  3. The gradient discretisation method for two-phase discrete fracture matrix models in deformable porous media.
    Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou, and Roland Masson.
    Finite volumes for complex applications IX, Springer Proc. Math. Stat. 8p, 2020.
    Preprint
  4. 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.
  5. The asymmetric gradient discretisation method.
    J. Droniou and R. Eymard.
    Finite volumes for complex applications VIII–-methods and theoretical aspects, Springer Proc. Math. Stat. 199, 311–319, 2017.
    Preprint
  6. Benchmark: two hybrid mimetic mixed schemes for the lid-driven cavity.
    Jérôme Droniou and Robert Eymard.
    Finite volumes for complex applications VIII–-methods and theoretical aspects, Springer Proc. Math. Stat. 199, 107–124, 2017.
    Preprint
  7. An error estimate for the approximation of linear parabolic equations by the gradient discretization method.
    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.
    Preprint
  8. Combining the hybrid mimetic mixed method and the Eulerian Lagrangian localised adjoint method for approximating miscible flows in porous media.
    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.
    Preprint
  9. Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model.
    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.
    Preprint
  10. Introduction to discrete functional analysis techniques for the numerical study of diffusion equations with irregular data.
    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.
    Preprint
  11. Uniform-in-time convergence of numerical schemes for Richards' and Stefan's models.
    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.
    Preprint
  12. A uniformly converging scheme for fractal conservation laws.
    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.
    Preprint
  13. Gradient schemes for an obstacle problem.
    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.
    Preprint
  14. Remarks on discretizations of convection terms in hybrid mimetic mixed methods.
    Jérôme Droniou.
    , 5 (3), 545–563, 2010, DOI: 10.3934/nhm.2010.5.545.
    Preprint
  15. Benchmark on Anisotropic Problems – Use of the mixed finite volume method.
    Claire Chainais-Hillairet, Jérôme Droniou, and Robert Eymard.
    Finite volumes for complex applications V (Aussois, 2008), 751–760, 2008.
    Preprint
  16. A recipe to couple two finite volume schemes for elliptic problems.
    Jérôme Droniou.
    Finite volumes for complex applications V (Aussois, 2008), 69–86, 2008.
    Preprint
  17. Fractal conservation laws: global smooth solutions and vanishing regularization.
    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.
    Preprint
  18. A finite volume scheme for noncoercive Dirichlet problems with right-hand sides in $H^-1$.
    Jérôme Droniou and Thierry Gallouët.
    Finite volumes for complex applications, III (Porquerolles, 2002), 181–188, 2002.
    Preprint
  19. 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. Robust Hybrid High-Order method on polytopal meshes with small faces.
    Jérôme Droniou and Liam Yemm.
    26p, 2021.
    Preprint
  2. An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincaré inequalities, and consistency.
    Daniele A. Di Pietro and Jérôme Droniou.
    55p, 2021.
    Preprint
  3. Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces.
    Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou, and Roland Masson.
    38p, 2020.
    Preprint
  4. Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media.
    Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou, and Roland Masson.
    36p, 2020.
    Preprint
  5. A combined GDM–ELLAM–MMOC scheme for advection dominated PDEs.
    Hanz Martin Cheng, Jérôme Droniou, and Kim-Ngan Le.
    35p, 2018.
    Preprint

Theses

Presentations

  • Convergence and error estimates of numerical schemes for the porous medium equation
    ANZIAM annual meeting, online, 4 February. slides.
  • Numerical analysis of two-phase flows models with mechanical deformation in fracture porous media
    AustMS annual meeting, UNE (Armidale, Australia), 10 December. slides.
  • Polynomial de Rham sequences of arbitrary degree on polyhedral meshes
    Seminar, Marseille (France), 8 December. slides.
  • High-order methods for linear and non-linear elliptic equations
    Algoritmy 2020 (plenary lecture), Podbanske (Slovakia), 10-15 September. slides.
  • Interplay between diffusion anisotropy and mesh skewness in Hybrid High-Order schemes
    FVCA9 (plenary lecture), Bergen (Norway), 15-19 June. slides.
  • A fully discrete exact de Rham sequence, with application to magnetostatics
    CTAC (regular presentation), UNSW (Sydney, Australia), 30 August - 2 September. slides.
  • B-char: an efficient (and feasible!) approach for mass-conserving characteristic schemes in 2D and 3D
    MWNDEA (regular presentation), Monash (Melbourne, Australia), 10-14 February. slides.

Teaching (last four years)

  • Real Analysis (2nd and 3rd year undergraduate): lectures (36h), applied class (12h) and coordination.
  • Numerical analysis and control of differential equations (Master): lectures (18h), applied class (6h) and coordination.
  • Real Analysis (2nd and 3rd year undergraduate): lectures (36h), applied class (22h) and coordination.
  • Differential Equations and Applications (2nd year undergraduate): lectures (18h) and coordination.
  • Real Analysis (2nd and 3rd year undergraduate): lectures (36h), applied class (22h) and coordination.
  • Differential Equations and Applications (2nd year undergraduate): lectures (18h) and coordination.
  • Partial Differential Equations (4th year - honours): lectures (18h).
  • Real Analysis (2nd and 3rd year undergraduate): lectures (36h), applied class (22h) and coordination.
  • Differential Equations and Applications (2nd year undergraduate): lectures (18h) and coordination.
  • Mathematics Research Project (3rd year undergraduate): 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 25/4/2021