Raphaèle Herbin's publications



WARNING Les publications les plus récentes sont sur HAL -- Most recent publications on the HAL server

Books or parts of book

Consistent Internal Energy Based Schemes for the Compressible Euler Equations

T. Gallouët, R. Herbin, J.-C. Latché, N. Therme,  

in Numerical Simulation in Physics and Engineering: Trends and Applications Springer, 2021


A Staggered Pressure Correction Numerical Scheme to Compute a Travelling Reactive Interface in a Partially Premixed Mixture.

D. Grapsas, R. Herbin, J.-C. Latché, Y. Nasseri,

In: Muñoz-Ruiz M.L., Parés C., Russo G. (eds) Recent Advances in Numerical Methods for Hyperbolic PDE Systems. SEMA SIMAI Springer Series, vol 28. Springer, Cham. (2021) https://doi.org/10.1007/978-3-030-72850-2_5


Non-conforming finite elements on polytopal meshes

Jérome Droniou, Robert Eymard, Thierry Gallouët, Raphaèle Herbin

In: Di Pietro D.A., Formaggia L., Masson R. (eds) Polyhedral Methods in Geosciences. SEMA SIMAI Springer Series, vol 27. Springer, 2021


Finite Volume Methods: Foundation and Analysis,

T. Barth, R. Herbin and M. Ohlberger, in "Encyclopedia of Computational Mechanics Second Edition", edited by Erwin Stein , Rene de Borst and Thomas J. R. Hughes. Chichester, UK: John Wiley and Sons, Ltd, pp. 1-60, 2018


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, Collection Mathématiques et Applications, Springer 2018


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)


Mesure, intégration et probabilités

T. Gallouët, R. Herbin,

Ellipses 2013 (updated version)


Polycopiés de cours


Equations aux dérivées partielles  

T. Gallouët, R. Herbin, polycopié de cours (Master 2)


Analysis of cell centered finite volume methods for incompressible fluid flows

Ecole de Printemps de Mecanique des Fluides Numerique, Roscoff,  Juin 2005.


Analyse numérique

R. Herbin,

polycopié de cours


Papers

Preprints

Convergence of the implicit MAC scheme of the incompressible Navier-Stokes equations with variable density and viscosity

L.Batteux, T. Gallouët, R. Herbin, J.-C Latché, P.Poullet

July 2021


A consistent quasi - second order staggered scheme for the two-dimensional shallow water equations

R. Herbin, J.-C Latché, Y. Nasseri, N. Therme

Submitted, April 2021


Published or to be published in journals

Lax-Wendroff consistency of finite volume schemes for systems of non linear conservation laws: extension to staggered schemes

Thierry Gallouët, R. Herbin, J.-C Latché

SeMA journal, 2021


Modelling of a spherical deflagration at constant speed

Dionysos Grapsas, Raphaèle Herbin, Jean-Claude Latché, Youssouf Nasseri

Computational and Applied Mathematics, 40:63,2021.


A unified analysis of elliptic problems with various boundary conditions and their approximation,

Jerome Droniou, Robert Eymard, Thierry Gallouët, Raphaèle Herbin

Czechoslovak Mathematical Journal Online firstDoi:   10.21136/CMJ.2019.0312-18


A decoupled staggered scheme for the shallow water equations

Raphaèle Herbin, Jean-Claude Latché, Youssouf Nasseri, Nicolas Therme

Proceedings of the Fifteenth International Conference Zaragoza-Pau on Mathematics Monografias Matematicas Garcia de Galdeano, 2020, hal-03039278.


A cell-centered scheme pressure-correction scheme for the compressible Euler equations,

Raphaèle Herbin,  Jean-Claude Latché,  Chady Zaza

IMA Journal of Numerical Analysis, 2019,Volume 40, Issue 3, July 2020, Pages 1792--1837, https://doi.org/10.1093/imanum/drz024


Consistent segregated staggered schemes with explicit steps for the isentropic and full Euler equations,

R. Herbin,  J.-C. Latché,  T.-T. Nguyen

M2AN, 2018, 52,3, 893-944, DOI: https://doi.org/10.1051/m2an/2017055


Convergence of the MAC scheme for the stationary compressible Navier-Stokes equations

T. Gallouët, R. Herbin, J.-C. Latché, D. Maltese, 

Math. Comp. 87 (2018) 1127-1163.


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. Stašova,

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,


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. Chénier, R. Eymard,  T. Gallouët,  R. Herbin,  Calcolo, 1-39, 2014.


Gradient schemes for the Stefan problem

R. Eymard, P. Féron, 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. Latché:


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. Latché.

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. Latché,

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. Latché,

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. Latché, 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. Latché

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. Chénier, 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. Latché, B.Piar,

Calcolo, vol. 44, 4, 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. Latché 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. Latché 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 Hérard, 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. Coudière, 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.


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.


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.


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. Latché 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. Latché

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.

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