Jerome Droniou

Assoc Professor

Accepting PhD Students

19992021
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Research Output 1999 2019

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2019

A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device

Botti, L., Di Pietro, D. A. & Droniou, J., 1 Jan 2019, In : Journal of Computational Physics. 376, p. 786-816 31 p.

Research output: Contribution to journalArticleResearchpeer-review

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A mixed finite element method for a sixth-order elliptic problem

Droniou, J., Ilyas, M., Lamichhane, B. P. & Wheeler, G. E., 1 Jan 2019, In : IMA Journal of Numerical Analysis. 39, 1, p. 374-397 24 p.

Research output: Contribution to journalArticleResearchpeer-review

An HMM–ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media

Cheng, H. M. & Droniou, J., 1 Jan 2019, In : Journal of Petroleum Science and Engineering. 172, p. 707-723 17 p.

Research output: Contribution to journalArticleResearchpeer-review

Open Access
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Convergence analysis of a family of ELLAM schemes for a fully coupled model of miscible displacement in porous media

Cheng, H. M., Droniou, J. & Le, K. N., Feb 2019, In : Numerische Mathematik. 141, 2, p. 353–397 45 p.

Research output: Contribution to journalArticleResearchpeer-review

Limits of the Stokes and Navier-Stokes equations in a punctured periodic domain

Chipot, M., Droniou, J., Planas, G., Robinson, J. C. & Xue, W., 1 Jan 2019, (Accepted/In press) In : Analysis and Applications.

Research output: Contribution to journalArticleResearchpeer-review

Numerical analysis of a two-phase flow discrete fracture matrix model

Droniou, J., Hennicker, J. & Masson, R., Jan 2019, In : Numerische Mathematik. 141, 1, p. 21–62 42 p.

Research output: Contribution to journalArticleResearchpeer-review

The Hessian Discretisation Method for Fourth Order Linear Elliptic Equations

Droniou, J., Lamichhane, B. P. & Shylaja, D., 2019, In : Journal of Scientific Computing. 78, 3, p. 1405-1437 33 p.

Research output: Contribution to journalArticleResearchpeer-review

Unified Convergence Analysis of Numerical Schemes for a Miscible Displacement Problem

Droniou, J., Eymard, R., Prignet, A. & Talbot, K. S., 2019, In : Foundations of Computational Mathematics. 19, 2, p. 333-374 42 p.

Research output: Contribution to journalArticleResearchpeer-review

2018

A gradient discretization method to analyze numerical schemes for nonlinear variational inequalities, application to the seepage problem

Alnashri, Y. & Droniou, J., 1 Jan 2018, In : SIAM Journal on Numerical Analysis. 56, 4, p. 2375-2405 31 p.

Research output: Contribution to journalArticleResearchpeer-review

A Hybrid High-Order discretisation of the Brinkman problem robust in the Darcy and Stokes limits

Botti, L., Di Pietro, D. A. & Droniou, J., 1 Nov 2018, In : Computer Methods in Applied Mechanics and Engineering. 341, p. 278-310 33 p.

Research output: Contribution to journalArticleResearchpeer-review

Analysis of miscible displacement through porous media with vanishing molecular diffusion and singular wells

Droniou, J. & Talbot, K. S., Jan 2018, In : Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 35, 1, p. 1-25 25 p.

Research output: Contribution to journalArticleResearchpeer-review

Open Access
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An arbitrary-order scheme on generic meshes for miscible displacements in porous media

Anderson, D. & Droniou, J., 1 Jan 2018, In : SIAM Journal on Scientific Computing. 40, 4, p. B1020-B1054 35 p.

Research output: Contribution to journalArticleResearchpeer-review

A third Strang lemma and an Aubin–Nitsche trick for schemes in fully discrete formulation

Di Pietro, D. A. & Droniou, J., 1 Sep 2018, In : Calcolo. 55, 3, 39 p., 40.

Research output: Contribution to journalArticleResearchpeer-review

Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes

Di Pietro, D. A., Droniou, J. & Manzini, G., 15 Feb 2018, In : Journal of Computational Physics. 355, p. 397-425 29 p.

Research output: Contribution to journalArticleResearchpeer-review

Improved L2 estimate for gradient schemes and super-convergence of the TPFA finite volume scheme

Droniou, J. D. R. & Nataraj, N., 17 Jul 2018, In : IMA Journal of Numerical Analysis. 38, 3, p. 1254-1293 40 p.

Research output: Contribution to journalArticleResearchpeer-review

Numerical Analysis for the Pure Neumann Control Problem Using the Gradient Discretisation Method

Droniou, J., Nataraj, N. & Shylaja, D., Oct 2018, In : Computational Methods in Applied Mathematics. 18, 4, p. 609-637 29 p.

Research output: Contribution to journalArticleResearchpeer-review

Open Access
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2017

A Hybrid High-Order method for Leray-Lions elliptic equations on general meshes

Di Pietro, D. A. & Droniou, J., 2017, In : Mathematics of Computation. 86, 307, p. 2159-2191 33 p.

Research output: Contribution to journalArticleResearchpeer-review

The gradient discretization method for optimal control problems, with superconvergence for nonconforming finite elements and mixed-hybrid mimetic finite differences

Droniou, J., Nataraj, N. & Shylaja, D., 2017, In : SIAM Journal on Control and Optimization. 55, 6, p. 3640-3672 33 p.

Research output: Contribution to journalArticleResearchpeer-review

2016

Convergence in C([0,T];L2(Ω)) of weak solutions to perturbed doubly degenerate parabolic equations

Droniou, J., Eymard, R. & Talbot, K. S., 5 Jun 2016, In : Journal of Differential Equations. 260, 11, p. 7821-7860 40 p.

Research output: Contribution to journalArticleResearchpeer-review

Gradient schemes: Generic tools for the numerical analysis of diffusion equations

Droniou, J., Eymard, R. & Herbin, R., 1 May 2016, In : Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique. 50, 3, p. 749-781 33 p.

Research output: Contribution to journalArticleResearchpeer-review

Gradient schemes for Stokes problem

Droniou, J., Eymard, R. & Feron, P., 1 Oct 2016, In : IMA Journal of Numerical Analysis. 36, 4, p. 1636-1669 34 p.

Research output: Contribution to journalArticleResearchpeer-review

Gradient schemes for the Signorini and the obstacle problems, and application to hybrid mimetic mixed methods

Alnashri, Y. & Droniou, J., 1 Dec 2016, In : Computers and Mathematics with Applications. 72, 11, p. 2788-2807 20 p.

Research output: Contribution to journalArticleResearchpeer-review

Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations

Droniou, J. & Eymard, R., 1 Apr 2016, In : Numerische Mathematik. 132, 4, p. 721-766 46 p.

Research output: Contribution to journalArticleResearchpeer-review

2015

A discontinuous-skeletal method for advection-diffusion-reaction on general meshes

Di Pietro, D. A., Droniou, J. & Ern, A., 2015, In : SIAM Journal on Numerical Analysis. 53, 5, p. 2135-2157 23 p.

Research output: Contribution to journalArticleResearchpeer-review

Gradient schemes for linear and non-linear elasticity equations

Droniou, J. & Lamichhane, B. P., 2015, In : Numerische Mathematik. 129, 2, p. 251-277 27 p.

Research output: Contribution to journalArticleResearchpeer-review

2014

Finite volume schemes for diffusion equations: introduction to and review of modern methods

Droniou, J., 2014, In : Mathematical Models and Methods in Applied Sciences. 24, 8, p. 1575 - 1619 45 p.

Research output: Contribution to journalArticleResearchpeer-review

On a miscible displacement model in porous media flow with measure data

Droniou, J. & Talbot, K., 2014, In : SIAM Journal on Mathematical Analysis. 46, 5, p. 3158 - 3175 18 p.

Research output: Contribution to journalArticleResearchpeer-review

2013

Gradient schemes: a generic framework for the discretisation of linear, nonlinear and nonlocal elliptic and parabolic equations

Droniou, J., Eymard, R., Gallouet, T. & Herbin, R., 2013, In : Mathematical Models and Methods in Applied Sciences. 23, 13, p. 2395 - 2432 38 p.

Research output: Contribution to journalArticleResearchpeer-review

2012

Convergence rate of the Allen-Cahn equation to generalized motion by mean curvature

Alfaro, M., Droniou, J. & Matano, H., 2012, In : Journal of Evolution Equations. 12, 2, p. 267 - 294 28 p.

Research output: Contribution to journalArticleResearchpeer-review

General fractal conservation laws arising from a model of detonations in gases

Alfaro, M. & Droniou, J., 2012, In : Applied Mathematics Research eXpress. 2012, 2, p. 127 - 151 25 p.

Research output: Contribution to journalArticleResearchpeer-review

2011

A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems

Da Veiga, B., Droniou, J. & Manzini, G., 2011, In : IMA Journal of Numerical Analysis. 31, 4, p. 1357 - 1401 45 p.

Research output: Contribution to journalArticleResearchpeer-review

Construction and convergence study of schemes preserving the elliptic local maximum principle

Droniou, J. & Le Potier, C., 2011, In : SIAM Journal on Numerical Analysis. 49, 2, p. 459 - 490 32 p.

Research output: Contribution to journalArticleResearchpeer-review

Finite-volume schemes for noncoercive elliptic problems with Neumann boundary conditions

Chainais-Hillairet, C. & Droniou, J., 2011, In : IMA Journal of Numerical Analysis. 31, 1, p. 61 - 85 25 p.

Research output: Contribution to journalArticleResearchpeer-review

2010

A numerical method for fractal conservation laws

Droniou, J., 2010, In : Mathematics of Computation. 79, 269, p. 95 - 124 30 p.

Research output: Contribution to journalArticleResearchpeer-review

A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods

Droniou, J., Eymard, R., Gallouet, T. & Herbin, R., 2010, In : Mathematical Models and Methods in Applied Sciences. 20, 2, p. 265 - 295 31 p.

Research output: Contribution to journalArticleResearchpeer-review

Remarks on discretizations of convection terms in hybrid mimetic mixed methods

Droniou, J., 2010, In : Networks and Heterogeneous Media. 5, 3, p. 545 - 563 19 p.

Research output: Contribution to journalArticleResearchpeer-review

The G method for heterogeneous anisotropic diffusion on general meshes

Agelas, L., Di Pietro, D. A. & Droniou, J., 2010, In : Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique. 44, 4, p. 597 - 625 29 p.

Research output: Contribution to journalArticleResearchpeer-review

2009

Noncoercive convection-diffusion elliptic problems with Neumann boundary conditions

Droniou, J. & Vazquez, J-L., 2009, In : Calculus of Variations and Partial Differential Equations. 34, 4, p. 413 - 434 22 p.

Research output: Contribution to journalArticleResearchpeer-review

Study of the mixed finite volume method for Stokes and Navier-Stokes equations

Droniou, J. & Eymard, R., 2009, In : Numerical Methods for Partial Differential Equations. 25, 1, p. 137 - 171 35 p.

Research output: Contribution to journalArticleResearchpeer-review

2007

Convergence analysis of a mixed finite volume scheme for an elliptic-parabolic system modeling miscible fluid flows in porous media

Chainais-Hillairet, C. & Droniou, J., 2007, In : SIAM Journal on Numerical Analysis. 45, 5, p. 2228 - 2258 31 p.

Research output: Contribution to journalArticleResearchpeer-review

Equivalence between entropy and renormalized solutions for parabolic equations with smooth measure data

Droniou, J. & Prignet, A., 2007, In : Nodea-Nonlinear Differential Equations and Applications. 14, 1-2, p. 181 - 205 25 p.

Research output: Contribution to journalArticleResearchpeer-review

Occurrence and non-appearance of shocks in fractal Burgers equations

Alibaud, N., Droniou, J. & Vovelle, J., 2007, In : Journal of Hyperbolic Differential Equations. 4, 3, p. 479 - 499 21 p.

Research output: Contribution to journalArticleResearchpeer-review

2006

A mixed finite volume scheme for anisotropic diffusion problems on any grid

Droniou, J. & Eymard, R., 1 Nov 2006, In : Numerische Mathematik. 105, 1, p. 35-71 37 p.

Research output: Contribution to journalArticleResearchpeer-review

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Fractal first-order partial differential equations

Droniou, J. & Imbert, C., 1 Oct 2006, In : Archive for Rational Mechanics and Analysis. 182, 2, p. 299-331 33 p.

Research output: Contribution to journalArticleResearchpeer-review

2004

An error estimate for the parabolic approximation of multidimentional scalar conservation laws with boundary conditions

Droniou, J., Imbert, C. & Vovelle, J., 1 Jan 2004, In : Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 21, 5, p. 689-714 26 p.

Research output: Contribution to journalArticleResearchpeer-review

2003

A finite volume scheme for a noncoercive elliptic equation with measure data

Droniou, J., Gallouët, T. & Herein, R., 1 Dec 2003, In : SIAM Journal on Numerical Analysis. 41, 6, p. 1997-2031 35 p.

Research output: Contribution to journalArticleResearchpeer-review

Convergence of a finite-volume mixed finite-element method for an elliptic-hyperbolic system

Droniou, J., Eymard, R., Hilhorst, D. & Zhou, X. D., 1 Jul 2003, In : IMA Journal of Numerical Analysis. 23, 3, p. 507-538 32 p.

Research output: Contribution to journalArticleResearchpeer-review

Error estimates for the convergence of a finite volume discretization of convection-diffusion equations

Droniou, J., 2 Jun 2003, In : Journal of Numerical Mathematics. 11, 1, p. 1-32 32 p.

Research output: Contribution to journalArticleResearchpeer-review