19992020

Research output per year

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Research Output

2020

An efficient implementation of mass conserving characteristic-based schemes in two and three dimensions

Cheng, H. M. & Droniou, J., 9 Apr 2020, In : SIAM Journal on Scientific Computing. 42, 2, p. A1071-A1096 26 p.

Research output: Contribution to journalArticleResearchpeer-review

A Unified Analysis of Elliptic Problems with Various Boundary Conditions and Their Approximation

Droniou, J., Eymard, R., Gallouët, T. & Herbin, R., Jun 2020, In : Czechoslovak Mathematical Journal. 70, 2, p. 339-368 30 p.

Research output: Contribution to journalArticleResearchpeer-review

High-order mass-lumped schemes for nonlinear degenerate elliptic equations

Droniou, J. & Eymard, R., 8 Jan 2020, In : SIAM Journal on Numerical Analysis. 58, 1, p. 153-188 36 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., Mar 2020, In : Analysis and Applications. 18, 2, p. 211-235 25 p.

Research output: Contribution to journalArticleResearchpeer-review

Preface

Di Pietro, D. A. & Droniou, J., 1 Jan 2020, Modeling, Simulation and Applications. Vol. 19. p. v-xxiii

Research output: Chapter in Book/Report/Conference proceedingForeword / PostscriptOtherpeer-review

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

Open Access
File
2 Citations (Scopus)

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

1 Citation (Scopus)

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
File
5 Citations (Scopus)

An Introduction to the Gradient Discretisation Method

Droniou, J., Eymard, R., Gallouët, T., Guichard, C. & Herbin, R., 1 Jan 2019, Numerical Mathematics and Advanced Applications ENUMATH 2017. Radu, F. A., Kumar, K., Berre, I., Nordbotten, J. M. & Pop, I. S. (eds.). Springer, Vol. 126. p. 451-459 9 p. (Lecture Notes in Computational Science and Engineering; vol. 126).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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

1 Citation (Scopus)

Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling

Droniou, J., Medla, M. & Mikula, K., 1 Dec 2019, In : Journal of Computational Physics. 398, p. 1-28 28 p., 108876.

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

1 Citation (Scopus)

The gradient discretisation method for linear advection problems

Droniou, J., Eymard, R., Gallouët, T. & Herbin, R., Oct 2019, (Accepted/In press) In : Computational Methods in Applied Mathematics. 23 p.

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

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

1 Citation (Scopus)

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

3 Citations (Scopus)

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

10 Citations (Scopus)

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
File
1 Citation (Scopus)

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

7 Citations (Scopus)

An eclectic view on numerical methods for PDEs: Presentation of the special issue "advanced Numerical Methods: Recent Developments, Analysis and Applications"

Antonietti, P. F., Droniou, J. & Eymard, R., 1 Jul 2018, In : Computational Methods in Applied Mathematics. 18, 3, p. 323-325 3 p.

Research output: Contribution to journalEditorialOtherpeer-review

Open Access
File

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

5 Citations (Scopus)

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

18 Citations (Scopus)

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

7 Citations (Scopus)

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
File
1 Citation (Scopus)

The Gradient Discretisation Method

Droniou, J., Eymard, R., Gallouet, T., Guichard, C. & Herbin, R., 2018, Cham Switzerland: Springer. 497 p. (Mathématiques et Applications; vol. 82)

Research output: Book/ReportBookResearchpeer-review

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

40 Citations (Scopus)

An error estimate for the approximation of linear parabolic equations by the gradient discretization method

Droniou, J., Eymard, R., Gallouët, T., Guichard, C. & Herbin, R., 2017, Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects. Cancès, C. & Omnes, P. (eds.). Cham Switzerland: Springer, Vol. 199. p. 371-379 9 p. (Springer Proceedings in Mathematics & Statistics; vol. 199).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

1 Citation (Scopus)

Benchmark: Two hybrid mimetic mixed schemes for the lid-driven cavity

Droniou, J. & Eymard, R., 2017, Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017. Cancès, C. & Omnes, P. (eds.). Cham Switzerland: Springer, Vol. 199. p. 107-124 18 p. (Springer Proceedings in Mathematics & Statistics; vol. 199).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

Combining the hybrid mimetic mixed method and the eulerian lagrangian localised adjoint method for approximating miscible flows in porous media

Cheng, H. M. & Droniou, J., 2017, Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems. Cancès, C. & Omnes, P. (eds.). Cham Switzerland: Springer, Vol. 200. p. 367-376 10 p. (Springer Proceedings in Mathematics & Statistics; vol. 200).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

2 Citations (Scopus)

The asymmetric gradient discretisation method

Droniou, J. & Eymard, R., 2017, Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017. Cancès, C. & Omnes, P. (eds.). Cham Switzerland: Springer, Vol. 199. p. 311-319 9 p. (Springer Proceedings in Mathematics & Statistics; vol. 199).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

2 Citations (Scopus)

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

3 Citations (Scopus)

Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model

Droniou, J., Hennicker, J. & Masson, R., 2017, Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017. Cancès, C. & Omnes, P. (eds.). Cham Switzerland: Springer, Vol. 199. p. 275-283 9 p. (Springer Proceedings in Mathematics & Statistics; vol. 199).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

1 Citation (Scopus)
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

7 Citations (Scopus)

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

30 Citations (Scopus)

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

9 Citations (Scopus)

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

7 Citations (Scopus)

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

23 Citations (Scopus)
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

37 Citations (Scopus)

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

11 Citations (Scopus)

Introduction to discrete functional analysis techniques for the numerical study of diffusion equations with irregular data

Droniou, J., 2015, Proceedings of the 17th Biennial Computational Techniques and Applications Conference. Cambridge University Press, Vol. 56. p. 101-127 27 p.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

2014

A uniformly converging scheme for fractal conservation laws

Droniou, J. & Jakobsen, E. R., 2014, Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Fuhrmann, J., Ohlberger, M. & Rohde, C. (eds.). Switzerland: Springer, Vol. 77. p. 237 - 245 9 p.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

4 Citations (Scopus)

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

124 Citations (Scopus)

Gradient schemes for an obstacle problem

Alnashri, Y. A. & Droniou, J., 2014, Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Fuhrmann, J., Ohlberger, M. & Rohde, C. (eds.). Switzerland: Springer, Vol. 77. p. 67 - 75 9 p.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

2 Citations (Scopus)

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

8 Citations (Scopus)

Uniform-in-time convergence of numerical schemes for Richards' and Stefan's models

Droniou, J., Eymard, R. & Guichard, C., 2014, Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Fuhrmann, J., Ohlberger, M. & Rohde, C. (eds.). Switzerland: Springer, Vol. 77. p. 247 - 254 8 p.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

1 Citation (Scopus)
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

79 Citations (Scopus)
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

3 Citations (Scopus)

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

5 Citations (Scopus)
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

33 Citations (Scopus)