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Raphaele Herbin

88
Documents

Presentation

Raphaèle Herbin professeur, Institut de Mathématiques de Marseille, I2M UMR 7373 Aix-Marseille Université.

Publications

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Convergence of the fully discrete incremental projection scheme for incompressible flows

Thierry Gallouët , Raphaèle Herbin , Jean-Claude Latché , David Maltese
Journal of Mathematical Fluid Mechanics, 2023, 25, pp.63. ⟨10.1007/s00021-023-00810-x⟩
Journal articles hal-03727713v2
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Convergence of the MAC scheme for the incompressible Navier-Stokes equations with variable density and viscosity

Léa Batteux , Thierry Gallouët , Raphaele Herbin , Jean-Claude Latche , Pascal Poullet
Mathematics of Computation, 2023, 92 (342), pp.1595-1631. ⟨10.1090/mcom/3803⟩
Journal articles hal-03312831v2
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A cell-centered pressure-correction scheme for the compressible Euler equations

Raphaele Herbin , Jean-Claude Latché , Chady Zaza
IMA Journal of Numerical Analysis, 2020, 40 (3), pp.1792-1837. ⟨10.1093/IMANUM/DRZ024⟩
Journal articles hal-01861734v2
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Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations

Thierry Gallouët , Raphaele Herbin , Jean-Claude Latché , David Maltese
Mathematics of Computation, 2018, 87, pp.1127-1163. ⟨10.1090/mcom/3260⟩
Journal articles hal-01342840v2
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Consistent segregated staggered schemes with explicit steps for the isentropic and full Euler equations

Raphaele Herbin , J.-C Latché , Trung Tan Nguyen
ESAIM: Mathematical Modelling and Numerical Analysis, 2018, 52 (3), pp.893-944. ⟨10.1051/m2an/2017055⟩
Journal articles hal-01436996v1
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Convergence of the MAC scheme for the incompressible Navier-Stokes equations

Thierry Gallouët , Raphaele Herbin , J.-C Latché , K. Mallem
Foundations of Computational Mathematics, 2018, 18 (1), pp.249-289. ⟨10.1007/s10208-016-9338-4⟩
Journal articles hal-01189014v4

Convergence of the marker-and-cell scheme for the semi-stationary compressible Stokes problem

Antonin Novotny , Thierry Gallouët , Raphaele Herbin , David Maltese
Mathematics and Computers in Simulation, 2017, 137, pp.325-349
Journal articles hal-01810434v1
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Analysis of a fractional-step scheme for the P1 radiative diffusion model

Raphaele Herbin , Thierry Gallouët , Jean-Claude Latché , Aurélien Larcher
Computational & Applied Mathematics, 2016, 35 (1), pp.135-151. ⟨10.1007/s40314-014-0186-z⟩
Journal articles hal-00477086v2
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Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations

Thierry Gallouët , Raphaèle Herbin , David Maltese , Antonin Novotny
IMA Journal of Numerical Analysis, 2016, 36 (2), pp.543-592. ⟨10.1093/imanum/drv028⟩
Journal articles hal-01108579v1
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Gradient schemes: generic tools for the numerical analysis of diffusion equations

Jérôme Droniou , Robert Eymard , Raphaele Herbin
ESAIM: Mathematical Modelling and Numerical Analysis, 2016, 50 (3), pp.749-781
Journal articles hal-01150517v2
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An unconditionally stable staggered pressure correction scheme for the compressible Navier-Stokes equations

D Grapsas , Raphaele Herbin , W Kheriji , J.-C Latché
SMAI Journal of Computational Mathematics, 2016, 2, pp.51-97. ⟨10.5802/smai-jcm.9⟩
Journal articles hal-01115250v1
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Applications of approximate gradient schemes for nonlinear parabolic equations

Robert Eymard , Angela Handlovicova , Raphaèle Herbin , Karol Mikula , O. Stašová
Applications of Mathematics, 2015, ⟨10.1007/s10492-015-0088-4⟩
Journal articles hal-00744767v1
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An extension of the MAC scheme to locally refined meshes : convergence analysis for the full tensor time-dependent Navier-Stokes equations

Eric Chénier , Robert Eymard , Thierry Gallouët , Raphaele Herbin
Calcolo, 2014, 52 (1), pp.69-107. ⟨10.1007/s10092-014-0108-x⟩
Journal articles hal-00751556v1
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On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations

Raphaele Herbin , Walid Kheriji , Jean-Claude Latché
ESAIM: Mathematical Modelling and Numerical Analysis, 2014, 48 (6), pp.1807-1857. ⟨10.1051/m2an/2014021⟩
Journal articles hal-00805510v2
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TP or not TP, that is the question

Robert Eymard , Thierry Gallouët , Cindy Guichard , Raphaèle Herbin , Roland Masson
Computational Geosciences, 2014, pp.18:285-296, 2014. ⟨10.1007/s10596-013-9392-9⟩
Journal articles hal-00801648v3
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Gradient schemes for two-phase flow in heterogeneous porous media and Richards equation

Robert Eymard , Cindy Guichard , Raphaèle Herbin , Roland Masson
Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2013, Volume 94, Issue 7-8, p. 560-585, July 2014. ⟨10.1002/zamm.201200206⟩
Journal articles hal-00740367v3
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Gradient schemes for the Stefan problem

Robert Eymard , Pierre Féron , Thierry Gallouët , Raphaèle Herbin , Cindy Guichard
International Journal on Finite Volumes, 2013, Volume 10 special
Journal articles hal-00751555v1
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Gradient schemes: a generic framework for the discretisation of linear, nonlinear and nonlocal elliptic and parabolic equations

Jérôme Droniou , Robert Eymard , Thierry Gallouët , Raphaèle Herbin
Mathematical Models and Methods in Applied Sciences, 2013, 13, pp.2395-2432
Journal articles hal-00751551v2
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A formally second order cell centered scheme for convection-diffusion equations on unstructured non-conforming grids

Libuse Piar , Fabrice Babik , Raphaele Herbin , Jean-Claude Latché
International Journal for Numerical Methods in Fluids, 2013, 71 (7), pp.873:890. ⟨10.1002/fld.3688⟩
Journal articles hal-00556911v2
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DISCONTINUOUS GALERKIN DISCRETIZATION AND HP-REFINEMENT FOR THE RESOLUTION OF THE NEUTRON TRANSPORT EQUATION

Raphaele Herbin , Damien Fournier , Romain Le Tellier
SIAM Journal on Scientific Computing, 2013, 35 (2), ⟨10.1137/110844581⟩
Journal articles hal-00781329v1
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Pressure correction staggered schemes for barotropic one-phase and two-phase flows

Walid Kheriji , Raphaele Herbin , Jean-Claude Latché
Computers and Fluids, 2013, 88, pp.524--542. ⟨10.1016/j.compfluid.2013.09.022⟩
Journal articles hal-00875348v1
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Small-stencil 3D schemes for diffusive flows in porous media

Robert Eymard , Cindy Guichard , Raphaele Herbin
ESAIM: Mathematical Modelling and Numerical Analysis, 2012, 46, pp.265-290. ⟨10.1051/m2an/2011040⟩
Journal articles hal-00542667v2
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Vertex-centred discretization of multiphase compositional Darcy flows on general meshes

Robert Eymard , Cindy Guichard , Raphaele Herbin , Roland Masson
Computational Geosciences, 2012, 16 (4), pp.987 - 1005. ⟨10.1007/s10596-012-9299-x⟩
Journal articles hal-00706244v1
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Vertex centred Discretization of Two-Phase Darcy flows on General Meshes

Robert Eymard , Cindy Guichard , Raphaele Herbin , Roland Masson
ESAIM: Proceedings, 2012, 35, pp.59-78. ⟨10.1051/proc/201235004⟩
Journal articles hal-00706246v1
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W1,q stability of the Fortin operator for the MAC scheme

Thierry Gallouët , Raphaele Herbin , Jean-Claude Latché
Calcolo, 2012, 49 (1), pp.63-71. ⟨10.1007/s10092-011-0045-x⟩
Journal articles hal-00673682v1
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Finite volume schemes for the biharmonic problem on general meshes

Robert Eymard , Thierry Gallouët , Raphaele Herbin , Alexander Linke
Mathematics of Computation, 2012, 81 (280), pp.2019-2048
Journal articles hal-00475419v2
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A discretization of phase mass balance in fractional step algorithms for the drift-flux model

Laura Gastaldo , Raphaele Herbin , Jean-Claude Latché
IMA Journal of Applied Mathematics, 2011, 31 (1), pp.116-146
Journal articles hal-00308838v1
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STAGGERED SCHEMES FOR ALL SPEED FLOWS

Raphaele Herbin , Walid Kheriji , Jean-Claude Latché
ESAIM: Proceedings, 2011, Congrès National de Mathématiques Appliquées et Industrielles, 35, pp.122-150. ⟨10.1051/proc/201235008⟩
Journal articles hal-00636173v1
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Approximation of the biharmonic problem using P1 finite elements

Robert Eymard , Raphaèle Herbin , Mohamed Rhoudaf
Journal of Numerical Mathematics, 2011, pp.Volume 19, Issue 1, Pages 1-26
Journal articles hal-00825673v1
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"A note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow" revisited

Raphaele Herbin , Ludovic Leclercq
Transportation Science, 2011, 45 (1), pp.138-142
Journal articles hal-00793622v1
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Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid interfaces

Robert Eymard , Thierry Gallouët , Raphaele Herbin
IMA Journal of Numerical Analysis, 2010, 30 (4), pp.1009-1043. ⟨10.1093/imanum/drn084⟩
Journal articles hal-00203269v5
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Approximation of the biharmonic problem using piecewise linear finite elements

Robert Eymard , Raphaèle Herbin
Comptes Rendus. Mathématique, 2010, 348 (23-24), pp.1283-1286. ⟨10.1016/j.crma.2010.11.002⟩
Journal articles hal-00693004v1
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Kinetic energy control in the MAC discretization of compressible Navier-Stokes equations

Raphaele Herbin , Jean-Claude Latché
International Journal on Finite Volumes, 2010, 7 (2)
Journal articles hal-00477079v1
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A convergent Finite Element-Finite Volume scheme for the compressible Stokes problem, Part II -- the isentropic case

Robert Eymard , Thierry Gallouët , Raphaele Herbin , Jean-Claude Latché
Math. Comp., 2010, 79 (270), pp.649--675. ⟨10.1090/S0025-5718-09-02310-2⟩
Journal articles hal-00359140v1
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Convergence of the MAC scheme for the compressible Stokes equations

Robert Eymard , Thierry Gallouët , Raphaele Herbin , Jean-Claude Latché
SIAM Journal on Numerical Analysis, 2010, 48 (6), pp.2218-2246. ⟨10.1137/090779863⟩
Journal articles hal-00542676v1
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An unconitionally stable finite-element/finite-volume pressure correction scheme for the drift-flux model

Laura Gastaldo , Raphaele Herbin , Jean-Claude Latché
ESAIM: Mathematical Modelling and Numerical Analysis, 2010, 44 (2), pp.251-287
Journal articles hal-00264659v1
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An unconditionnally stable pressure correction scheme for compressible barotropic Navier-Stokes equations

Thierry Gallouët , Laura Gastaldo , Jean-Claude Latché , Raphaele Herbin
ESAIM: Mathematical Modelling and Numerical Analysis, 2010, 44 (2), pp.251--287. ⟨10.1051/m2an/2010002⟩
Journal articles hal-00179610v1
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A unified approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume methods

Jerome Droniou , Robert Eymard , Thierry Gallouët , Raphaele Herbin
Mathematical Models and Methods in Applied Sciences, 2010, 20 (2), pp.265--295. ⟨10.1142/S0218202510004222⟩
Journal articles hal-00346077v1
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A collocated finite volume scheme to solve free convection for general non-conforming grids

Eric Chénier , Robert Eymard , Raphaele Herbin
Journal of Computational Physics, 2009, 228 (6), pp.2296-2311. ⟨10.1016/j.jcp.2008.10.034⟩
Journal articles hal-00280822v2
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Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral grids

Robert Eymard , Thierry Gallouët , Raphaele Herbin
Journal of Numerical Mathematics, 2009, 17 (3), pp.173--193. ⟨10.1515/JNUM.2009.010⟩
Journal articles hal-00351867v1
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A convergent Finite Element-Finite Volume scheme for the compressible Stokes problem Part I -- the isothermal case

Thierry Gallouët , Raphaele Herbin , Jean-Claude Latché
Mathematics of Computation, 2009, 78 (267), pp.1333-1352
Journal articles hal-00198724v2
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A nine point finite volume scheme for the simulation of diffusion in heterogeneous media

Léo Agélas , Robert Eymard , Raphaele Herbin
Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2009, 347 (11-12), pp.673-676
Journal articles hal-00350139v1
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Convergence analysis of a locally stabilized collocated finite volume scheme for incompressible flows

Robert Eymard , Raphaele Herbin , Jean-Claude Latché , Bruno Piar
ESAIM: Mathematical Modelling and Numerical Analysis, 2009, 43 (5), pp.889-927. ⟨10.1051/m2an/2009031⟩
Journal articles hal-00530814v1
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Discretization of the coupled heat and electrical diffusion problems by the finite element and the finite volume methods

Abdallah Bradji , Raphaele Herbin
IMA Journal of Numerical Analysis, 2008, 28 (3), pp.469-495. ⟨10.1093/imanum/drm030⟩
Journal articles hal-00123247v1
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A fast precipitation and dissolution reaction for a reaction diffusion system arising in a porous medium

Nicolas Bouillard , Robert Eymard , Marie Henry , Raphaele Herbin , Danielle Hilhorst
ESAIM: Mathematical Modelling and Numerical Analysis, 2007, 41 (6), pp.975-1000. ⟨10.1051/m2an:2007047⟩
Journal articles hal-00136237v1
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A new colocated finite volume scheme for the incompressible Navier-Stokes equations on general non matching grids

Robert Eymard , Raphaele Herbin
Comptes Rendus. Mathématique, 2007, ⟨10.1016/j.crma.2007.03.025⟩
Journal articles hal-02505888v1
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Convergence analysis of a colocated finite volume scheme for the incompressible Navier-Stokes equations on general 2 or 3D meshes

Robert Eymard , Raphaele Herbin , Jean-Claude Latché
SIAM Journal on Numerical Analysis, 2007, 45 (1), pp.1-36. ⟨10.1137/040613081⟩
Journal articles hal-00004841v2
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On the stability of colocated clustered finite volume simplicial discretizations for the 2D Stokes problem

Robert Eymard , Raphaele Herbin , Jean-Claude Latché , Bruno Piar
Calcolo, 2007, 44 (4), pp.219-234. ⟨10.1007/s10092-007-0138-8⟩
Journal articles hal-00136127v1
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A cell-centred finite volume approximation for second order partial derivative operators with full matrix on unstructured meshes in any space dimension

Robert Eymard , Thierry Gallouët , Raphaèle Herbin
IMA Journal of Numerical Analysis, 2006, 26, pp.326-353
Journal articles hal-00004840v1
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On a stabilized colocated Finite Volume scheme for the Stokes problem

Robert Eymard , Raphaele Herbin , Jean-Claude Latché
ESAIM: Mathematical Modelling and Numerical Analysis, 2006, 40 (3), pp.501-527. ⟨10.1051/m2an:2006024⟩
Journal articles hal-00793601v1
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A staggered finite volume scheme on general meshes for the generalized Stokes problem in two space dimensions AstaggeredschemefortheStokesequations

Philippe Blanc , Robert Eymard , Raphaèle Herbin
International Journal on Finite Volumes, 2005, 2 (1), pp.1-31
Journal articles hal-01112399v1
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A staggered finite volume scheme on general meshes for the Navier-Stokes equations in two space dimensions

Robert Eymard , Raphaèle Herbin
International Journal on Finite Volumes, 2005, 2 (1), pp.1-18
Journal articles hal-01112401v1
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Axisymmetric finite volumes for the numerical simulation of bulk CO 2 transport and assimilation in a leaf

Emily Gallouët , Raphaèle Herbin
International Journal on Finite Volumes, 2005, 4 (2), pp.1-17
Journal articles hal-01112397v1
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The Lions domain decomposition algorithm on non matching cell-centered finite volume meshes

René Cautrès , Raphaèle Herbin , Florence Hubert
IMA Journal of Numerical Analysis, 2004, 24, pp.465 - 490
Journal articles hal-00003306v1
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Convergence of linear finite elements for diffusion equations with measure data

Thierry Gallouët , Raphaele Herbin
Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, vol. 338, issue 1, pp 81-84
Journal articles hal-00003437v1
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A finite volume scheme for anisotropic diffusion problems

Robert Eymard , Thierry Gallouët , Raphaele Herbin
Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, vol. 339, issue 4, pp.299-302
Journal articles hal-00003328v1
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A finite volume scheme for noncoercive elliptic equation with measure data

Jerome Droniou , Thierry Gallouët , Raphaele Herbin
SIAM Journal on Numerical Analysis, 2003, 41 (6), pp.1997-2031. ⟨10.1137/S0036142902405205⟩
Journal articles hal-00003440v1
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Des mathématiciens découvrent les volumes finis

Isabelle Faille , Thierry Gallouët , Raphaele Herbin
Matapli, 1991, 28, pp.37-48
Journal articles hal-03140480v1
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A DECOUPLED STAGGERED SCHEME FOR THE SHALLOW WATER EQUATIONS

Raphaèle Herbin , Jean-Claude Latché , Youssouf Nasseri , Nicolas Therme
Fifteenth International Conference Zaragoza-Pau on Mathematics and its Applications, Sep 2018, Jaca, Spain
Conference papers hal-02163454v2
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A class of staggered schemes for the compressible Euler equations

Raphaele Herbin , Jean-Claude Latché
NMA, 2018, Borovets, Bulgaria
Conference papers hal-02019553v1
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An error estimate for the approximation of linear parabolic equations by the Gradient Discretization Method

Jérôme Droniou , Robert Eymard , Thierry Gallouët , Cindy Guichard , Raphaele Herbin
FVCA 2017 - International Conference on Finite Volumes for Complex Applications VIII, 2017, Lille, France
Conference papers hal-01442921v1
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Results with a Locally Refined MAC-Like Scheme - Benchmark Session

Eric Chénier , Robert Eymard , Raphaele Herbin
Finite Volumes for Complex Applications 8, Jun 2017, Lille, France. pp.2182 - 139
Conference papers hal-01546509v1
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Low Mach number limit of a pressure correction MAC scheme for compressible barotropic flows

Raphaele Herbin , J.-C. Latché , K Saleh
Finite Volumes for Complexe Applicxations 8, Jun 2017, Lille, France. ⟨10.1007/978-3-319-57397-7_18⟩
Conference papers hal-01482309v2
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TWO MODELS FOR THE COMPUTATION OF LAMINAR FLAMES IN DUST CLOUDS

Dionysios C Grapsas , Raphaele Herbin , J C Latché
Finite volume for Complex Applications 8, Jun 2017, Lille, France
Conference papers hal-01483466v1
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Convergence of the mac scheme for variable density flows

Thierry Gallouët , Raphaele Herbin , Jean-Claude Latché , K Mallem
Finite Volume for Complex Applications 8, Jun 2017, Lille, France
Conference papers hal-01483467v1

Vertex-centred Discretization of Multiphase Compositional Darcy Flows on General Meshes

Cindy Guichard , Robert Eymard , Raphaele Herbin , Roland Masson , P Samier
ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery, Sep 2012, Biarritz, France. ⟨10.3997/2214-4609.20143221⟩
Conference papers hal-01238550v1

Multiphase Flow in Porous Media Using the VAG Scheme

Robert Eymard , Cindy Guichard , Raphaele Herbin , Roland Masson
Finite Volumes for Complex Applications VI Problems & Perspectives, Jun 2011, Prague, Czech Republic. pp.409-417, ⟨10.1007/978-3-642-20671-9_43⟩
Conference papers hal-01238557v1
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Discretization of the viscous dissipation term with the MAC scheme

Fabrice Babik , Raphaele Herbin , Walid Kheriji , Jean-Claude Latché
FVCA 6, Internal Symposium, Jun 2011, Prague, Czech Republic. pp.571-579, ⟨10.1007/978-3-642-20671-9_60⟩
Conference papers hal-00576268v1
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Playing with Burgers's equation

Thierry Gallouët , Raphaele Herbin , Jean-Claude Latché , Trung Tan Nguyen
Finite Volumes for Complex Applications VI - Problems & Perspectives, Jun 2011, Prague, Czech Republic. pp.523-531, ⟨10.1007/978-3-642-20671-9_55⟩
Conference papers hal-00576248v1
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Staggered discretizations, pressure correction schemes and all speed barotropic flows

Laura Gastaldo , Raphaele Herbin , Walid Kheriji , Céline Lapuerta , Jean-Claude Latché
FVC6, International Symposium, Jun 2011, Prague, Czech Republic. pp.839-855, ⟨10.1007/978-3-642-20671-9_86⟩
Conference papers hal-00576246v1
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Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids

Raphaele Herbin , Florence Hubert
Finite volumes for complex applications V, Jun 2008, France. pp.659--692
Conference papers hal-00429843v1
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Development of numerical methods for the reactive transport of chemical species in a porous media : a nonlinear conjugate gradient method

Nicolas Bouillard , Philippe Montarnal , Raphaele Herbin
2005, pp.16
Conference papers hal-00113144v1
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The gradient discretisation method

Jérôme Droniou , Robert Eymard , Thierry Gallouët , Cindy Guichard , Raphaele Herbin
Springer International Publishing AG, 82, 2018, Mathématiques et Applications, M. Hoffmann et V. Perrier, 978-3-319-79042-8. ⟨10.1007/978-3-319-79042-8⟩
Books hal-01382358v8
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MESURE, INTEGRATION, PROBABILITES

Thierry Gallouët , Raphaele Herbin
Ellipses Edition Marketing, 678 p., 2013, 978-2-7298-77538
Books hal-01283567v2
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Consistent Internal Energy Based Schemes for the Compressible Euler Equations

Thierry Gallouët , Raphaele Herbin , J.-C Latché , N Therme
David Greiner, Maria Isabel Asensio, Rafael Montenegro. Numerical Simulation in Physics and Engineering: Trends and Applications, 1st ed. 2021 Lecture Notes of the XVIII ‘Jacques-Louis Lions' Spanish-French School, 24, Springer, 2021, SEMA SIMAI Springer Series
Book sections hal-01553699v2
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Non-conforming finite elements on polytopal meshes

Jerome Droniou , Robert Eymard , Thierry Gallouët , Raphaèle Herbin
Prof. Daniele Antonio Di Pietro, Prof. Luca Formaggia, Prof. Roland Masson. Polyhedral Methods in Geosciences, Springer, 2021, SEMA SIMAI Springer Series, 978-3-030-69362-6
Book sections hal-02898897v1
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Finite Volume Methods

Robert Eymard , Thierry Gallouët , Raphaèle Herbin
J. L. Lions; Philippe Ciarlet. Solution of Equation in ℝn (Part 3), Techniques of Scientific Computing (Part 3), 7, Elsevier, pp.713-1020, 2000, Handbook of Numerical Analysis, 9780444503503. ⟨10.1016/S1570-8659(00)07005-8⟩
Book sections hal-02100732v2