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
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
J. Droniou, R. Eymard, T. Gallouët, R. Herbin, C. Guichard, Collection Mathématiques et Applications, Springer 2018
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.
R. Herbin,
polycopié de cours
Papers
Preprints
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
Thierry Gallouët, R. Herbin, J.-C Latché
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
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
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.
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
J. Droniou, R. Eymard, T. Gallouët, R. Herbin,
Math. Models Methods Appl. Sci. (M3AS), 23, 2013, 13, 2395-2432.
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.
T. Gallouet, R. Herbin, J.-C. Latché,
short note IJFV 2010
L. Gastaldo, R. Herbin and and J. C. Latché.
ESAIM: M2AN (2010) DOI: 10.1051/m2an/2010002.
R. Eymard, T. Gallouët, R. Herbin and and J. C. Latché.
Math of Comp (2010)
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
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.
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.
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.
T. Gallouët, L. Gastaldo, R. Herbin, J.-C. Latché
Math. Model. Numer. Anal., 42, 2, 303-331, 2008.
A. Bradji, R. Herbin,
IMA J. Numer. Anal., 28, 3, 469--495, 2008.
E. Chénier, R. Eymard and R. Herbin, O. Touazi,
Int. J. Numer. Meth. Fluids 2008; 56:2045-2068.
R. Eymard, R. Herbin, J.C. Latché, B.Piar,
Calcolo, vol. 44, 4, 219-234, 2007.
N. Bouillard, R. Eymard, M. Henry, R. Herbin, D. Hilhorst
Nonlinear Analysis: Real World Applications 10 (2009) 629-638.
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.
R. Eymard, T. Gallouët, and R. Herbin.
C.R., Math., Acad. Sci. Paris, 2007, 344(6):403�40
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/
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.
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,
Modelling CO2 diffusion and assimilation in a leaf with axisymmetric finite volumes,
E. Gallouët and R. Herbin, IJFV 2005
Ph. Blanc, R. Eymard and R. Herbin, Int. J. Finite Volumes, March 2005
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
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
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)
R. Eymard, T. Gallouët, M. Gutnik, R. Herbin and D. Hilhorst, M3AS, 9, 2001.
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.
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
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.
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.
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.
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).
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).
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.
Existence of a Solution to a Coupled Elliptic System. T. Gallouët & R. Herbin Appl. Math. Lett., 7 (2), pp. 49-55, 1994.
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).
A uniqueness result for measure-valued solutions to nonlinear hyperbolic equations,
T. Gallouët. & R. Herbin
Int. Diff. Equations, 6, 6, 1383-1394 (1993).
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
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,
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
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
A finite volume scheme on general meshes for the steady Navier-Stokes equations in two space dimensions
Enumath, Prague 2003
R. Eymard, R Herbin
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.
``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.
``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.
``A 3-dimensional planar SOFC stack model" M. Bernier, J.R. Ferguson, R. Herbin,
3rd European SOFC Forum, Nantes, v1, 315-324, 1998.
"Convergence of finite volume schemes for semilinear convection diffusion equations"R. Eymard, T. Gallouët, R. Herbin,
Workshop on Finite Volume Methods, Madrid, 1998
"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
"Numerical approximation of a nonlinear problem with a Signorini boundary condition,
in Iterative Methods, Laramie, USA, July 1997,
R. Herbin & E. Marchand.
"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.
"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.
"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.
"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.
"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.