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1

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

Jérôme Droniou, Robert Eymard

Journal:

Numerical Methods for Partial Differential Equations

Year:

2009

Language:

english

File:

PDF, 596 KB

english, 2009

2

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

Droniou, Jerome

Journal:

Mathematical Models and Methods in Applied Sciences

Year:

2014

Language:

english

File:

PDF, 990 KB

english, 2014

3

Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes

Di Pietro, Daniele A., Droniou, Jérôme, Manzini, Gianmarco

Journal:

Journal of Computational Physics

Year:

2018

Language:

english

File:

PDF, 1.11 MB

english, 2018

4

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

Di Pietro, Daniele A., Droniou, Jérôme

Journal:

Year:

2018

Language:

english

File:

PDF, 777 KB

english, 2018

5

Fractal First-Order Partial Differential Equations

Jérôme Droniou, Cyril Imbert

Journal:

Archive for Rational Mechanics and Analysis

Year:

2006

Language:

english

File:

PDF, 348 KB

english, 2006

6

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

Jérôme Droniou, Robert Eymard

Journal:

Numerische Mathematik

Year:

2006

Language:

english

File:

PDF, 678 KB

english, 2006

7

Noncoercive convection–diffusion elliptic problems with Neumann boundary conditions

Jérôme Droniou, Juan-Luis Vázquez

Journal:

Calculus of Variations and Partial Differential Equations

Year:

2009

Language:

english

File:

PDF, 328 KB

english, 2009

8

Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle

Droniou, Jérôme, Potier, Christophe Le

Journal:

SIAM Journal on Numerical Analysis

Year:

2011

Language:

english

File:

PDF, 859 KB

english, 2011

9

A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS

DRONIOU, JÉRÔME, EYMARD, ROBERT, GALLOUËT, THIERRY, HERBIN, RAPHAÈLE

Journal:

Mathematical Models and Methods in Applied Sciences

Year:

2010

Language:

english

File:

PDF, 325 KB

english, 2010

10

A Finite Volume Scheme for a Noncoercive Elliptic Equation with Measure Data

Jérôme Droniou , Thierry Gallouët and Raphaèle Herbin

Journal:

SIAM Journal on Numerical Analysis

Year:

2004

Language:

english

File:

PDF, 924 KB

english, 2004

11

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

Journal:

SIAM Journal on Numerical Analysis

Year:

2007

Language:

english

File:

PDF, 2.54 MB

english, 2007

12

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

Droniou, Jérôme, Eymard, Robert

Journal:

Numerische Mathematik

Year:

2016

Language:

english

File:

PDF, 884 KB

english, 2016

13

Unified Convergence Analysis of Numerical Schemes for a Miscible Displacement Problem

Droniou, Jérôme, Eymard, Robert, Prignet, Alain, Talbot, Kyle S.

Journal:

Foundations of Computational Mathematics

Year:

2018

Language:

english

File:

PDF, 3.18 MB

english, 2018

14

Finite volume methods for convection-diffusion equations with right-hand side in H -1

Droniou, Jérôme, Gallouët, Thierry

Journal:

ESAIM Mathematical Modelling and Numerical Analysis

Year:

2002

Language:

english

File:

PDF, 216 KB

english, 2002

15

A density result in Sobolev spaces

Jérôme Droniou

Journal:

Journal de Mathématiques Pures et Appliquées

Year:

2002

Language:

english

File:

PDF, 192 KB

english, 2002

16

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

Jérôme Droniou, Alain Prignet

Journal:

Nonlinear Differential Equations and Applications NoDEA

Year:

2007

Language:

english

File:

PDF, 262 KB

english, 2007

17

Non-coercive Linear Elliptic Problems

Jérôme Droniou

Journal:

Potential Analysis

Year:

2002

Language:

english

File:

PDF, 183 KB

english, 2002

18

Parabolic Capacity and Soft Measures for Nonlinear Equations

Jérôme Droniou, Alessio Porretta, Alain Prignet

Journal:

Potential Analysis

Year:

2003

Language:

english

File:

PDF, 432 KB

english, 2003

19

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

Matthieu Alfaro, Jérôme Droniou, Hiroshi Matano

Journal:

Journal of Evolution Equations

Year:

2012

Language:

english

File:

PDF, 561 KB

english, 2012

20

A Finite Volume Scheme for a Noncoercive Elliptic Equation with Measure Data

Droniou, Jérôme, Gallouët, Thierry, Herbin, Raphaèle

Journal:

SIAM Journal on Numerical Analysis

Year:

2003

Language:

english

File:

PDF, 380 KB

english, 2003

21

Convergence Analysis of a Mixed Finite Volume Scheme for an Elliptic-Parabolic System Modeling Miscible Fluid Flows in Porous Media

Chainais-Hillairet, Claire, Droniou, Jérôme

Journal:

SIAM Journal on Numerical Analysis

Year:

2007

Language:

english

File:

PDF, 1.83 MB

english, 2007

22

GRADIENT SCHEMES: A GENERIC FRAMEWORK FOR THE DISCRETISATION OF LINEAR, NONLINEAR AND NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS

DRONIOU, JEROME, EYMARD, ROBERT, GALLOUET, THIERRY, HERBIN, RAPHAELE

Journal:

Mathematical Models and Methods in Applied Sciences

Year:

2013

Language:

english

File:

PDF, 561 KB

english, 2013

23

Gradient schemes for linear and non-linear elasticity equations

Droniou, Jérôme, Lamichhane, Bishnu P.

Journal:

Numerische Mathematik

Year:

2015

Language:

english

File:

PDF, 374 KB

english, 2015

24

On a Miscible Displacement Model in Porous Media Flow with Measure Data

Droniou, Jérôme, Talbot, Kyle S.

Journal:

SIAM Journal on Mathematical Analysis

Year:

2014

Language:

english

File:

PDF, 309 KB

english, 2014

25

OCCURRENCE AND NON-APPEARANCE OF SHOCKS IN FRACTAL BURGERS EQUATIONS

ALIBAUD, NATHAËL, DRONIOU, JÉRÔME, VOVELLE, JULIEN

Journal:

Journal of Hyperbolic Differential Equations

Year:

2007

Language:

english

File:

PDF, 341 KB

english, 2007

26

Global and Local Estimates for Nonlinear Noncoercive Elliptic Equations with Measure Data

Droniou, Jérôme

Journal:

Communications in Partial Differential Equations

Year:

2003

Language:

english

File:

PDF, 323 KB

english, 2003

27

A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes

Di Pietro, Daniele A., Droniou, Jérôme, Ern, Alexandre

Journal:

SIAM Journal on Numerical Analysis

Year:

2015

Language:

english

File:

PDF, 437 KB

english, 2015

28

Gradient Schemes for Stokes problem

Droniou, Jérôme, Eymard, Robert, Feron, Pierre

Journal:

IMA Journal of Numerical Analysis

Year:

2015

Language:

english

File:

PDF, 460 KB

english, 2015

29

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

Droniou, Jérôme, Eymard, Robert, Talbot, Kyle S.

Journal:

Journal of Differential Equations

Year:

2016

Language:

english

File:

PDF, 1.61 MB

english, 2016

30

A numerical method for fractal conservation laws

Droniou, Jérôme

Journal:

Mathematics of Computation

Year:

2010

Language:

english

File:

PDF, 498 KB

english, 2010

31

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

Alnashri, Yahya, Droniou, Jérôme

Journal:

Computers & Mathematics with Applications

Year:

2016

Language:

english

File:

PDF, 1.50 MB

english, 2016

32

The G method for heterogeneous anisotropic diffusion on general meshes

Agélas, Léo, Di Pietro, Daniele A., Droniou, Jérôme

Journal:

ESAIM Mathematical Modelling and Numerical Analysis

Year:

2010

Language:

english

File:

PDF, 469 KB

english, 2010

33

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

Droniou, Jérome, Eymard, Robert, Herbin, Raphaèle

Journal:

ESAIM Mathematical Modelling and Numerical Analysis

Year:

2016

Language:

english

File:

PDF, 663 KB

english, 2016

34

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

Droniou, Jérôme, Talbot, Kyle S.

Journal:

Annales de l'Institut Henri Poincare (C) Non Linear Analysis

Year:

2017

Language:

english

File:

PDF, 1.26 MB

english, 2017

35

Ws,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

Di Pietro, Daniele A., Droniou, Jérôme

Journal:

Mathematical Models and Methods in Applied Sciences

Year:

2017

Language:

english

File:

PDF, 525 KB

english, 2017

36

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

Di Pietro, Daniele A., Droniou, Jérôme

Journal:

Mathematics of Computation

Year:

2016

Language:

english

File:

PDF, 502 KB

english, 2016

37

The Gradient Discretization Method for Optimal Control Problems, with Superconvergence for Nonconforming Finite Elements and Mixed-Hybrid Mimetic Finite Differences

Droniou, Jérome, Nataraj, Neela, Shylaja, Devika

Journal:

SIAM Journal on Control and Optimization

Year:

2017

Language:

english

File:

PDF, 619 KB

english, 2017

38

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

Botti, Lorenzo, Di Pietro, Daniele A., Droniou, Jérôme

Journal:

Computer Methods in Applied Mechanics and Engineering

Year:

2018

Language:

english

File:

PDF, 3.51 MB

english, 2018

39

Improved $L^2$ estimate for gradient schemes and super-convergence of the TPFA finite volume scheme

Droniou, Jérôme, Nataraj, Neela

Journal:

IMA Journal of Numerical Analysis

Year:

2018

Language:

english

File:

PDF, 799 KB

english, 2018

40

An Arbitrary-Order Scheme on Generic Meshes for Miscible Displacements in Porous Media

Anderson, Daniel, Droniou, Jérôme

Journal:

SIAM Journal on Scientific Computing

Year:

2018

Language:

english

File:

PDF, 1.68 MB

english, 2018

41

[Mathématiques et Applications] The Gradient Discretisation Method Volume 82 ||

Droniou, Jérôme, Eymard, Robert, Gallouët, Thierry, Guichard, Cindy, Herbin, Raphaèle

Year:

2018

File:

PDF, 8.26 MB

2018

42

An Eclectic View on Numerical Methods for PDEs: Presentation of the Special Issue “Advanced Numerical Methods: Recent Developments, Analysis and Applications”

Antonietti, Paola F., Droniou, Jérôme, Eymard, Robert

Journal:

Computational Methods in Applied Mathematics

Year:

2018

Language:

english

File:

PDF, 436 KB

english, 2018

43

[Mathématiques et Applications] The Gradient Discretisation Method Volume 82 || Non Degenerate Parabolic Problems

Droniou, Jérôme, Eymard, Robert, Gallouët, Thierry, Guichard, Cindy, Herbin, Raphaèle

Year:

2018

Language:

english

File:

PDF, 614 KB

english, 2018

44

[Mathématiques et Applications] The Gradient Discretisation Method Volume 82 || Conforming Approximations

Droniou, Jérôme, Eymard, Robert, Gallouët, Thierry, Guichard, Cindy, Herbin, Raphaèle

Year:

2018

Language:

english

File:

PDF, 544 KB

english, 2018

45

[Mathématiques et Applications] The Gradient Discretisation Method Volume 82 || Hybrid Mimetic Mixed Schemes

Droniou, Jérôme, Eymard, Robert, Gallouët, Thierry, Guichard, Cindy, Herbin, Raphaèle

Year:

2018

Language:

english

File:

PDF, 419 KB

english, 2018

46

The Hessian Discretisation Method for Fourth Order Linear Elliptic Equations

Droniou, Jérôme, Lamichhane, Bishnu P., Shylaja, Devika

Journal:

Journal of Scientific Computing

Year:

2018

Language:

english

File:

PDF, 722 KB

english, 2018

47

A Gradient Discretization Method to Analyze Numerical Schemes for Nonlinear Variational Inequalities, Application to the Seepage Problem

Alnashri, Yahya, Droniou, Jérôme

Journal:

SIAM Journal on Numerical Analysis

Year:

2018

Language:

english

File:

PDF, 890 KB

english, 2018

48

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

Botti, Lorenzo, Di Pietro, Daniele A., Droniou, Jérôme

Journal:

Journal of Computational Physics

Year:

2018

Language:

english

File:

PDF, 1.92 MB

english, 2018

49

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

Cheng, Hanz Martin, Droniou, Jérôme, Le, Kim-Ngan

Journal:

Numerische Mathematik

Year:

2018

Language:

english

File:

PDF, 812 KB

english, 2018

50

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

Droniou, Jérôme, Hennicker, Julian, Masson, Roland

Journal:

Numerische Mathematik

Year:

2018

Language:

english

File:

PDF, 1.07 MB

english, 2018