Raphaèle Herbin's publications

Books or parts of book

Finite Volume Methods: Foundation and Analysis,
T. Barth, R. Herbin and M. Ohlberger, à paraitre dans Encyclopedia of Computational Mechanics, 2017, Wiley

The Gradient Discretization Method: : A framework for the discretisation of linear and nonlinear elliptic and parabolic problems,
J. Droniou, R. Eymard, T. Gallouët, R. Herbin, C. Guichard, under revision, 2017

Finite Volume Methods,
R. Eymard, T. Gallouët, R. Herbin,
Handbook for Numerical Analysis, Ph. Ciarlet, J.L. Lions eds, North Holland, 2000, 715-1022.
(version with a few corrections and addenda)

Analysis of cell centered finite volume methods for incompressible fluid flows
Ecole de Printemps de Mecanique des Fluides Numerique, Roscoff,  Juin 2005.

Mesure, intégration et probabilités
T. Gallouët, R. Herbin,
Ellipses 2013

Polycopiés de cours


Equations aux dérivées partielles  
T. Gallouët, R. Herbin, polycopié de cours (Master 2)

Analyse numéique
R. Herbin,
polycopé de cours

Papers

Preprints
Entropy estimates for a class of schemes for the Euler equations,
T. Gallouët, R. Herbin,  J.-C. Latché,  N. Therme
submitted 2017.


On some consistent explicit staggered  schemes for the shallow water and Euler equations,
R. Herbin,  J.-C. Latché,  T.-T. Trung
2016 under revision.

A cell-centered pressure-correction scheme for the compressible Euler equations
R. Herbin,  J.-C. Latché,  C. Zaza,
2015 under revision.

Published or to be published in journals
Convergence of the MAC scheme for the stationary compressible Navier-Stokes problem
T. Gallouët, R. Herbin, J.-C. Latche, D. Maltese, 
to appear in Math. of Comp.

Convergence of the Marker-and-Cell scheme for a semi-stationary compressible Navier-Stokes problem
T. Gallouët, R. Herbin, D. Maltese and A. Novotny, 
Mathematics and Computers in Simulation, 2017, vol. 137, issue C, 325-349

An unconditionally stable staggered pressure correction scheme for the compressible Navier-Stokes equations,
D. Grapsas, R. Herbin,  J.-C. Latché,  W. Kheriji
SMAI-Journal of computational mathematics, 2 (2016), p. 51-97.

Convergence of the Marker-and-Cell scheme for the incompressible Navier-Stokes problem
R. Herbin,  J.-C. Latché,  K. Mallem
Foundations of Computational Mathematics, 2016, pp. 1-41

Gradient schemes: Generic tools for the numerical analysis of diffusion equations
J. Droniou, R. Eymard, R. Herbin, ESAIM: M2AN, 50,3, 749-781, 2016.
DOI: http://dx.doi.org/10.1051/m2an/2015079

Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations
T. Gallouet, R. Herbin, D. Maltese and A. Novotny,
IMA J Numer Anal (2016) 36 (2): 543-592.

Applications of approximate gradient schemes for nonlinear parabolic equations
R. Eymard,  A. Handlovicova,  R. Herbin,   K. Mikula  O. Stašov�,
Applications of Mathematics, 60, 2, 135-156, 2015.

RTk mixed finite elements for some nonlinear problems
R. Eymard, T. Gallouet,  R. Herbin,
Mathematics of computation, doi:10.1016/j.matcom.2014.11.013, published online  12 December 2014

Analysis of a fractional-step scheme for the P1 radiative diffusion
T. Gallouët, R. Herbin, A. Larcher, J.-C. Latché, accepted for publication in COAM.

On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations. < R. Herbin,  W. Kheriji, J.-C. Latché
ESAIM: Mathematical Modelling and Numerical Analysis, 48, 06, 2014, pp. 1807--1857,
published on line, April 2014
 

TP or not TP, that is the question
R. Eymard, T. Gallouet,  C. Guichard, R. Herbin, R. Masson,
Computational Geoscience, 1-12, 2014

Gradient schemes for two-phase flow in heterogeneous porous media and Richards equation
R. Eymard, C. Guichard, R. Herbin, R. Masson, 
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift fëur Angewandte Mathematik und Mechanik, 94, 7-8, 560--585, 2014.

An extension of the MAC scheme to locally refined meshes : convergence analysis for the full tensor time–dependent Navier–Stokes equations
E. Ch�nier, R. Eymard,  T. Gallouët,  R. Herbin,  Calcolo, 1-39, 2014.

Gradient schemes for the Stefan problem
R. Eymard, P. F�ron, T. Gallouet, R. Herbin, and C. Guichard.
Int. J. Finite Vol., 10, 2013.

Pressure correction staggered schemes for barotropic one-phase and two-phase flows
W. Kheriji, R. Herbin, J.-C. Latché
Computers & Fluids, Volume 88,  2013, Pages 524-542

Gradient schemes: a generic framework for the discretisation of linear, nonlinear and nonlocal elliptic and parabolic equations
J. Droniou, R. Eymard,  T. Gallouët,  R. Herbin, 
Math. Models Methods Appl. Sci. (M3AS), 23, 2013, 13, 2395-2432.

Discontinuous Galerkin discretization and hp-refinement for the resolution of the neutron transport equation
D. Fournier, R. Herbin, R. Le Tellier,  Journal on Scientific Computing,  2013, Vol. 35, No. 2 : pp. A936-A956


A formally second order cell centered scheme for convection-diffusion equations on general grids.
International Journal for Numerical Methods in Fluids 71, 873–890 (2013) L. Piar, F. Babik, R. Herbin, J.-C. Latch\eacute:

Vertex-centred Discretization of Multiphase Compositional Darcy flows on General Meshes
R. Eymard, C. Guichard, R. Herbin, R. Masson,
Computational Geosciences 16, 4 (2012) 987-1005


W1,q stability of the Fortin operator for the MAC scheme
T. Gallouët, R. Herbin, J.-C. Latch\eacute, 
Calcolo, Volume 49, Issue 1 (2012), Page 63-71.


Finite volume schemes for the biharmonic problem on general meshes
R. Eymard, T. Gallouët, R. Herbin, A. Linke,
Math. of Comp., 81(280):2019-2048, 2012.

Small-stencil 3D schemes for diffusive flows in porous media,
R. Eymard, C. Guichard and R. Herbin
ESAIM: Mathematical Modelling and Numerical Analysis, 46 , pp 265-290 doi:10.1051/m2an/2011040 (2012).

Convergence of the MAC scheme for the compressible Stokes equations,
R. Eymard, T. Gallouët, R. Herbin, J.-C. Latché,
SIAM J. Numer. Anal. 48, pp. 2218-2246 (29 pages), published online 2010

A note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow'' revisited,
R. Herbin, L. Leclercq,
short note, Transportation Science Vol. 45, No. 1, February 2011, pp. 138-142

Approximation of the biharmonic problem using P1 finite elements.
R. Eymard, R. Herbin, and M. Rhoudaf,
J. of Num. Math., 19(1):1-26, 2011.

Kinetic energy control in explicit Finite Volume discretizations of the incompressible and compressible Navier-Stokes equations
T. Gallouet, R. Herbin, J.-C. Latché,
short note  IJFV 2010

An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux equation
L. Gastaldo, R. Herbin and and J. C. Latch\é.
ESAIM: M2AN (2010)  DOI: 10.1051/m2an/2010002.

A convergent Finite Element-Finite Volume scheme for the compressible Stokes problem. Part II -- the isentropic case
R. Eymard, T. Gallouët, R. Herbin and and J. C. Latché.
Math of Comp (2010)

A Unified Approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume Methods ,
J. Droniou, R. Eymard, T. Gallouët, and R. Herbin.
Mathematical Models and Methods in Applied Sciences,  Vol. 20, No. 2 (2010) 1--31.  DOI: 10.1142/S0218202510004222

Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral grids ,
R. Eymard, T. Gallouët, and R. Herbin,
Journal of Numerical Mathematics, Volume 17, Issue 3, Pages 173–193, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: 10.1515/JNUM.2009.010, /October/2009.

A convergent Finite Element-Finite Volume scheme for the compressible Stokes problem, Part I -- the isothermal case,
T. Gallouët, R. Herbin and J.C. Latch\é,
Math. Comp. 78 (2009), 1333-1352.

A collocated finite volume scheme to solve free convection for general non-conforming grids,
E. Ch�nier, R. Eymard, R. Herbin
Journal of Computational Physics, Volume 228, Issue 6, 1 April 2009, Pages 2296-2311.

A discretization of the phase mass balance in fractional step algorithms for the drift-flux model,,
L. Gastaldo,   R. Herbin, J.-C. Latch\é,
IMA Journal of Numerical Analysis, 2011, 31(1), 116--146. Advance Access published on September 7, 2009; doi: doi:10.1093/imanum/drp006


A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media,
L. Agelas, R. Eymard,  and R. Herbin,  Comptes rendus de l'Acad�mie des Sciences Math�matique 2009, vol. 347, no11-12, pp. 673-676

Convergence of a locally stabilized collocated finite volume scheme for incompressible flows, ,
R. Eymard,   J.C. Latch\é, R. Herbin and B. Piar,
M2AN 43 (2009) 889-927.

Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid interfaces, ,
R. Eymard, T. Gallouët, R. Herbin,
IMA J Numer Anal
2010) 30(4): 1009-1043  first published on June 16, 2009; doi: doi:10.1093/imanum/drn084


Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids, ,
R. Herbin, F. Hubert,
Finite Volumes for Complex Applications V, R. Eymard and J.-M. Herard eds, Wiley, 2008, pp. 659-692.

An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations,
T. Gallouët, L. Gastaldo, R. Herbin, J.-C. Latch\é
Math. Model. Numer. Anal., 42, 2, 303-331, 2008.
Discretization of coupled heat and electrical diffusion problems by finite-element and finite-volume methods
A. Bradji, R. Herbin,
IMA J. Numer. Anal., 28, 3, 469--495, 2008.

Collocated finite volume schemes for the simulation of  natural convective flows on unstructured meshes,
E. Ch\énier, R. Eymard and R. Herbin, O. Touazi,
Int. J. Numer. Meth. Fluids 2008; 56:2045-2068.

On the stability of collocated clustered finite volume simplicial discretizations for the 2D Stokes problem,
R. Eymard, R. Herbin, J.C. Latch\é, B.Piar,
Calcolo, vol. 44, N�4, pp. 219-234, 2007, 

A fast precipitation and dissolution reaction for a reaction diffusion system arising in a porous medium
N. Bouillard, R. Eymard, M. Henry, R. Herbin, D. Hilhorst
Nonlinear Analysis: Real World Applications 10 (2009) 629-638.

Diffusion with dissolution and precipitation in a porous media: mathematical analysis and numerical approximation of a simplified model,
N. Bouillard, R. Eymard, R. Herbin Ph. Montarnal
M2AN,41,6,975-1000,2007.

Combined triangular FV-triangular FE method for nonlinear convection-diffusion problems,
M. Bejcek, M. Feistauer, T. Gallouët, J. Hajek, R. Herbin,
ZAMM Z. Angew. Math. Mech. 87 (2007), no. 7, 499-517.

A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis. 
R. Eymard, T. Gallouët, and R. Herbin.
C.R., Math., Acad. Sci. Paris, 2007, 344(6):403�40

A new colocated finite volume scheme for the incompressible Navier-Stokes equations on general non matching grids.
R. Eymard and R. Herbin.
C. R. Math. Acad. Sci. Paris, 344(10):659�662, 2007.

< Analysis tools for finite volume schemes
Proceedings of  Equadiff, Brastislava August 2005,
Acta
Mathematica Universitatis Comenianae http://www.iam.fmph.uniba.sk/amuc/
Convergence analysis of a colocated  finite volume scheme for the  incompressible Navier-Stokes equations on  general 2 or 3D meshes
 R. Eymard,  J.C. Latch\é and R. Herbin,  August 2004,   SIAM J. Numer. Anal. 45, 1 (2007)

On a stabilized colocated Finite Volume scheme for the Stokes problem
R. Eymard,  J.C. Latch\é and R. Herbin, M2AN 40, 3, 2006 pp 501-527.
    

A cell-centred finite volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension,
 R. Eymard, T. Gallouët and R. Herbin,
IMA Journal of Numerical Analysis  26,  2, 326-353 IMAJNA 2006 


Lateral Diffusion of CO2 in Leaves is not Sufficient to Support Photosynthesis,
J. Morison, E. Gallouët, T. Lawson, G. Cornic, R. Herbin & N. Baker, 
Plant. Phys 2005 

Modelling CO2 diffusion and assimilation in a leaf with axisymmetric finite volumes,
E. Gallouët and R. Herbin,  IJFV 2005 

A staggered finite volume scheme on general meshes for the generalized Stokes problem in two space dimensions
Ph. Blanc, R. Eymard and R. Herbin,
Int. J. Finite Volumes, March 2005

A staggered finite volume scheme on general meshes for the Navier-Stokes equations in two space dimensions,
R. Eymard and R. Herbin,
Int. J. Finite Volumes, March 2005

A finite volume for anisotropic diffusion problems,
R. Eymard, T. Gallouët and R. Herbin,
CRAS Vol 339/4 pp 299-302, 2004

An error estimate for finite volume methods for the Stokes equations on equilateral triangular meshes,
Ph. Blanc, R. Eymard and R. Herbin, Num. Meth. PDE, Published Online: 8 Apr 2004


Convergence of linear finite elements for diffusion equations with measure data,
T. Gallouët and R. Herbin, C. R. Math. Acad. Sci. Mathematiques, vol. 338, issue 1, 1er janvier 2004, pp. 81-84. 

The Lions domain decomposition algorithm on non  matching cell-centered finite volume meshes,
R. Cautres, R. Herbin and F. Hubert, 
  Preprint LATP 02/27,  IMA Journal of Numerical Analysis, 24, 465-490, 2004.

Mathematical study of a petroleum-engineering scheme,
R. Eymard, R. Herbin and A. Michel,  ESAIM: M2AN, vol 37,  no 6, 2003, pp 937-972.


A finite volume scheme  for a noncoercive elliptic equation with measure data
J. Droniou, T. Gallouët and 
R. Herbin,
SIAM Journal on Numerical Analysis Volume 41, Number 6 pp. 1997-2031, 2003

A cell-centered finite volume scheme on general meshes for the Stokes equations in two space dimensions,
R. Eymard  and R. Herbin,  
C. R. Math. Acad. Sci. Paris, 337,2,125--128, 2003

A monotony method for the numerical solution of some free boundary problems,
R. Herbin,
SIAM J. Numer. Anal., 40,6,  2292--2310, 2003,  http://www.siam.org/journals/sinum/40-6/38055.html

Upwind finite volume schemes for one and two dimensional Euler Equations,  
T. Gallouët ,
JM H�rard, R.. Herbin, N. Jullian and N. Seguin, AIAA-2003-4122.

Error estimate for approximate solutions of a nonlinear convection-diffusion problem,
R. Eymard, T. Gallouët, R. Herbin, Advances in Differential Equations, 7, 4, 2002, 419-440

Convergence of a finite volume scheme for nonlinear degenerate parabolic equations
R. Eymard, T. Gallouët, R. Herbin and A. Michel,
Numer. Math., 92, 1, 41--82 (2002)

Approximation by the finite volume method of an elliptic-parabolic equation arising in environmental studies,
R. Eymard, T. Gallouët, M. Gutnik, R. Herbin and D. Hilhorst, M3AS, 9, 2001.


Discrete Sobolev inequalities and Lp error estimates for approximate finite volume solutions of convection diffusion equations,
Y. Coudi�re, T. Gallouët, R. Herbin,
M2AN, 35, 4, 767-778, 2001.


Finite volume approximation of a class of variational inequalities,
R. Herbin, E. Marchand, IMA Journal of Numerical Analysis (2001) 21, 553-585.

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Finite volume approximation of elliptic problems and convergence of an approximate gradient,
R. Eymard, T. Gallouët, R. Herbin,  Appl. Num. Math., 37/1-2,  pp. 31 - 53, 2001.

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Error estimates for the approximate finite volume solution of convection diffusion equations with general boundary conditions, T. Gallouët, R. Herbin, M.H. Vignal,
SIAM J. Numer. Anal., 37, 6, 1935 - 1972, 2000.
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Convergence of finite volume schemes for semilinear convection diffusion equations,
R. Eymard, T. Gallouët, R. Herbin,
Numerische Mathematik, 82, 91-116, 1999
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Existence of the solution to an elliptic system with a Signorini boundary condition, 
S. Gerbi, R. Herbin & E. Marchand,
Advances in Differential Equations, 4, 2, 225-250, 1999.
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An error estimate for a finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh,
R. Eymard, T. Gallouët, M. Ghilani, R. Herbin,IMA Journal of Numerical Analysis (1998), 18, 563-594.
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Comparison of finite volume and finite element discretizations for the discretization of elliptic and hyperbolic equations,
R. Herbin & O. Labergerie,
Comput. Methods Appl. Mech. Engrg., 147, 85-103, 1997.
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Interaction fluide structure active~: �coulement art�riel, J. Ohayon, P. Teppaz & R. Herbin
C.R. Acad. Sciences, t. 324, S�rie II b, 37-45, 1997, biomecanique.


A mathematical model of solid oxide fuel cells, J.R. Ferguson, J.M. Fiard & R. Herbin,
Journal of Power Sources 58, 109-122, (1996).
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Existence and uniqueness of the entropy solution to a nonlinear hyperbolic equation,
R. Eymard, T. Gallouët. & R. Herbin,
Chin. Ann. of Math., 16B: 1, 1-14 (1995).
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Nonuniform cavity pressure model and ventricular mechanics,
R. Chadwick, R. Herbin & J. Ohayon,
Mech. Res. Comm. 22, 3, 205-219, 1995.

An error estimate for a four point finite volume scheme for the convection-diffusion equation on a triangular mesh, R. Herbin,
  Num. Meth. P.D.E., 165-173, 1995.
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Existence of a Solution to a Coupled Elliptic System.
T. Gallouët & R. Herbin Appl. Math. Lett., 7 (2), pp. 49-55, 1994.
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Comparison between finite volume and finite element methods for the numerical simulation of an elliptic problem arising in electrochemical engineering, .
J.M. Fiard & R. Herbin  Comput. Methods Appl. Mech. Engrg. 115, 315-338, 1994.

Convergence of an Upstream Finite Volume Scheme for a Nonlinear Hyperbolic Equation on a Triangular Mesh. 
S. Champier, T. Gallouët. & R. Herbin,
Numerische Mathematik 66, pp 139-157 (1993).
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A uniqueness result for measure-valued solutions to nonlinear hyperbolic equations,
T. Gallouët. & R. Herbin
Int. Diff. Equations, 6, 6, 1383-1394 (1993). 
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On the effective resistance of an electrolytic membrane, Math. Engng. Ind., 4, 4, 311-326, 1993.

Proceedings

Explicit staggered schemes for the compressible euler equations
R. Herbin, J.-C. Latch\é and T.T. Nguyen
ESAIM: PROCEEDINGS, Juillet 2013, Vol. 40, p. 83-102

Staggered schemes for all speed flows
R. Herbin, W. Kheriji and J.-C. Latch\é
ESAIM: PROCEEDINGS, March 2012, Vol. 35, p. 122-150

3D Benchmark  on discretization schemes for anisotropic diffusion problem on general grids,
Eymard, R., Henry G., Herbin R., Hubert F., Klofkorn R., and Manzini G.,
 Proceedings of Finite Volumes for Complex Applications VI, 2011


Unstructured cell centred schemes for the Navier Stokes equations,
FVCA4, Marrakech, July 2005. publi�  dans Proceedings of FVCA4, F. Benkahldoun Ed., Hermes-Penton,
R Herbin
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Development of numerical methods for the reactive transport of chemical species in a porous media : a nonlinear conjugate gradient method
Coupled Problems, Santorin, May 2005, published in the proceedings of the International Conference on coupled problems in Science and Engineering,
M. Papadrakis, E. Onate and B. Shrefer Eds, CIMNE, Barcelona, 2005.
  N. Bouillard,  Ph. Montarnal   &   R. Herbin,
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Diffusion with dissolution and precipitation in  a porous media, approximation by a finite volume scheme,
FVCA4, Marrakech, July 2005. publi�  dans Proceedings of FVCA4, F. Benkahldoun Ed., Hermes-Penton,
N. Bouillard, R. Eymard, R Herbin and Ph. Montarnal
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Modelling $CO_2$ diffusion and assimilation in a leaf with  axisymmetric finite volumes,
FVCA4, Marrakech, July 2005. publi�  dans Proceedings of FVCA4, F. Benkahldoun Ed., Hermes-Penton,
E. Gallouët, R Herbin
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A finite volume scheme on general meshes  for the steady Navier-Stokes equations in two space dimensions
Enumath,  Prague 2003
R. Eymard, R Herbin
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A Neumann-Neumann method using a finite volume discretization" R. Cautres, T.Gallouët, S. Gerbi, R. Herbin,
Proceedings of the 13th International Conference on Domain Decomposition Methods,
N. Debit, M. Garbey, R. Hoppe, J. Periaux, D. Keyes and Y. Kuznetsov eds, 205-212, 2000. 
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``Non-matching finite volume grids and the non overlapping Scharz algorithm" R. Cautres, R. Herbin, F. Hubert
Proceedings of the 13th International Conference on Domain Decomposition Methods}, N. Debit, M. Garbey, R. Hoppe, J. Periaux, D. Keyes and Y. Kuznetsov eds, 213-219, 2000.
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``Numerical approximation of an elliptic-parabolic equation arising in environment" R. Eymard, T.Gallouët, M. Gutnic, R. Herbin, D.Hilhorst
Computing and Vizualisation in Science, 3:33-38 (2000) Springer Verlag.

 
``Instantaneous and noninstantaneous dissolution: approximation  by the finite volume method" , Eymard, R. and Gallouët, T. and Herbin, R. and Hilhorst, D. and Mainguy, M., Actes du 30�me Congr�s d'Analyse Num�rique: CANum '98  (Arles, 1998), ESAIM Proc., 6, 41--55 (electronic), Soc. Math. Appl. Indust., Paris, 1999.

``Finite volume approximation of elliptic problems with irregular data" T.Gallouët, R. Herbin,
Finite Volume for Complex Analysis, Duisburg, 1999, Hermes.
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``A 3-dimensional planar SOFC stack model" M. Bernier, J.R. Ferguson, R. Herbin,
3rd European SOFC Forum, Nantes, v1, 315-324, 1998.
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"Convergence of finite volume schemes for semilinear convection diffusion equations"R. Eymard, T. Gallouët, R. Herbin,
Workshop on Finite Volume Methods, Madrid, 1998
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"Instantaeous and noninstantaneous dissolution: approximation by the finite volume method"R. Eymard, T. Gallouët, R. Herbin, D. Hilhorst and M. Mainguy
ESAIM Proceedings, Actes du 30eme congres d'analyse numerique, CANum'98, 1998
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"Numerical approximation of a nonlinear problem with a Signorini boundary condition,
in Iterative Methods, Laramie, USA, July 1997,
R. Herbin & .E. Marchand.
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"Finite volume methods for diffusion convection equations on general meshes",
Finite volumes for complex applications, Problems and Perspectives, F. Benkhaldoun and R. Vilsmeier eds, Hermes, 1996, 153-160.
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"Stack and cell modelling with SOFC3D: a computer program for the 3D simulations of solid oxide fuel cells", 2nd European Solid Oxide Fuel Cell Forum, en collaboration avec M. Bernier et E. Gehain, May 6-10, 1996, Oslo, Norway.
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"3D Numerical simulation of the temperature, potential and concentration distribution of a unit cell for various geometries of SOFC's," European Solid Oxide Fuel Cell Forum, en collaboration avec J.M. Fiard et J.R. Ferguson, Oct 3-7, 1994, Lucerne, Switzerland.
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"Schemas de volumes finis pour les problemes d'ecoulements en milieu poreux, en collaboration avec R. Eymard et T. Gallouët, Journees numeriques de Besancon, 1994.
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"A four point finite volume scheme for the convection-diffusion equation on a triangular mesh, en collaboration avec O. Labergerie Proceedings of the 3rd International Colloquium on Numerical Analysis, Plovdiv, 1994, Lucerne, Switzerland.
"Existence of the solution to a nonlinear system arising in the modelling of fuel cells, Proceedings of the 5th International
Colloquium on Differential Equations, Plovdiv, Bulgaria, 1994.

"Convergence of a finite volume scheme for a nonlinear hyperbolic equation". Proceedings of the Third colloquium on numerical analysis, 1995 pp. 61-70. with R. Eymard et T. Gallouët.
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Books or parts of books

"Analysis of cell centered finite volume methods for incompressible fluid flows",
Ecole de Printemps de M�canique des Fluides Num�rique, Roscoff,  Juin 2005.
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"The finite volume method",  R. Eymard, T. Gallouët, R. Herbin,
Handbook for Numerical Analysis, Ph. Ciarlet J.L. Lions eds, North Holland, 2000, 715-1022
.
(version contenant quelques ajouts et corrections typographiques)
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"Mesure et int�gration ", T. Gallouët, R. Herbin,  polycopié de cours et exercices corrigés de licence.
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"Cours d'analyse num�rique ",  R. Herbin, polycopi� de cours et exercices corrig�s de licence.
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Cours d'analyse numérique des EDP,
, R. Herbin,
polycopié de cours et exercices corrigés de master 1ère année (in French).