Books
or parts of books
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 with a few correrctions and addenda)
Analysis of cell
centered finite volume methods for incompressible fluid flows
Ecole de
Printemps de
Mécanique des Fluides Numérique,
Roscoff, Juin 2005.
Mesure, intégration et probabilités
T.
Gallouët, R. Herbin,
Cours
d'analyse numérique,
R. Herbin, polycopié
de cours et exercices corrigés
de licence.
Cours
d'analyse numérique des EDP, R. Herbin, polycopié
de cours et exercices corrigés de
master 1ère année.
Papers
Submitted
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, submitted, 2011.
Vertex-centred Discretization of Multiphase Compositional Darcy flows on General Meshes
R. Eymard, C. Guichard, R. Herbin, R. Masson, submitted, 2011.
A
second order cell centered scheme for convection-diffusion equations on
unstructured non–conforming grids
L. Piar, F. Babik, R. Herbin, J.-C. Latché, submitted, 2011.
A
kinetic energy preserving convection operator for the MAC
discretization of compressible Navier-Stokes equations,
R. Herbin, J.-C. Latché, submitted, 2010.
Kinetic
energy control in explicit Finite Volume discretizations of the
incompressible and compressible Navier-Stokes equations
T. Gallouët, R. Herbin, J.-C. Latché, short note,
submitted,
2010.
Analysis
of a fractional-step scheme for the P1 radiative diffusion
model,
T. Gallouët, R. Herbin, A. Larcher, J.-C.
Latché, 2009.
Published or to be published
in journals
W1,q
stability of the
Fortin operator for the MAC scheme
T. Gallouët, R. Herbin,
J.-C. Latché, 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, to appear in Math.
of=m Comp.
Small-stencil
3D schemes for diffusive flows in porous media,
R.
Eymard, C. Guichard and R. Herbin (2012). Small-stencil 3D schemes for
diffusive flows in porous media. ESAIM: Mathematical Modelling and
Numerical Analysis, 46 , pp 265-290 doi:10.1051/m2an/2011040 .
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
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. Chénier, 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'Académie des Sciences Mathématique 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 Advance Access 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
M2AN
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, N°4, pp.
219-234, 2007,
A fast precipitation
and dissolution reaction for a
reactiondiffusion 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):40340
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):659662, 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 df
file
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
ps
file
pdf file
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
ps
file
pdf
file
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.
ps
file,
pdf
file
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
ps
file,
pdf
file
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)
ps
file,
pdf
file,
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.
ps
file
pdf
file
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.
ps
file
pdf
file
Finite
volume approximation of a class of variational inequalities, R.
Herbin, E. Marchand, IMA
Journal of Numerical Analysis
(2001) 21,
553-585.
ps
file
pdf
file
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.
ps
file
pdf
file
Approximation by the finite volume method of an
elliptic-parabolic equation arising in environmental studies, R.
Eymard,
R. and Gallouët, T. and Herbin, R. and Gutnic, M.
and
Hilhorst, D., Math. Models
Methods Appl. Sci.,
11,9, 1505--1528, 2001
ps
file
pdf
file
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.
ps
file
pdf
file
Convergence
of finite volume schemes for semilinear convection diffusion
equations,
R.
Eymard, T. Gallouët, R. Herbin,
Numerische Mathematik, 82,
91-116, 1999
psfile
pdffile
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.
ps
file
pdf
file
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.
ps
file
pdf
file
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.
ps
file
pdf
file
Interaction
fluide structure active~: écoulement artériel, J.
Ohayon,
P. Teppaz & R. Herbin
C.R. Acad. Sciences, t. 324,
Série 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).
ps
file
pdf
file
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).
ps
file
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.
ps
file
pdf
file
Existence
of a Solution to a Coupled Elliptic System. T. Gallouët &
R. Herbin
Appl. Math. Lett., 7
(2), pp. 49-55, 1994.
ps
file
pdf
file
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).
ps
file
pdf
file
A
uniqueness result for measure-valued solutions to nonlinear hyperbolic
equations, T. Gallouët. & R.
Herbin
Int. Diff. Equations, 6, 6,
1383-1394
(1993).
ps
file
pdf
file
On
the effective resistance of an electrolytic membrane, Math.
Engng. Ind., 4, 4, 311-326, 1993.
Proceedings
Unstructured cell
centred schemes for the Navier Stokes equations,
FVCA4,
Marrakech, July
2005. publié dans Proceedings
of FVCA4, F. Benkahldoun Ed., Hermes-Penton,
R
Herbin
ps
file
pdf file
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,
ps
file
pdf
file
Diffusion with dissolution and precipitation in a porous
media, approximation by a finite volume scheme,
FVCA4,
Marrakech, July
2005. publié dans Proceedings
of FVCA4, F. Benkahldoun Ed., Hermes-Penton,
N.
Bouillard,
R. Eymard, R Herbin and
Ph. Montarnal
ps
file
pdf file
Modelling $CO_2$ diffusion and assimilation in a leaf
with axisymmetric finite volumes,
FVCA4,
Marrakech, July
2005. publié dans Proceedings
of FVCA4, F. Benkahldoun Ed., Hermes-Penton,
E.
Gallouët, R Herbin
ps
file
pdf file
A finite volume scheme on general meshes for the steady
Navier-Stokes equations in two space dimensions
Enumath,
Prague
2003
R.
Eymard, R
Herbin
ps
file
pdf file
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.
ps
file
pdf file
``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.
ps
file
pdf
file
``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 30ème Congrès d'Analyse
Numérique:
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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filefile
pdffile
``A
3-dimensional planar SOFC stack model" M. Bernier, J.R. Ferguson,
R. Herbin,
3rd European SOFC Forum,
Nantes, v1,
315-324, 1998.
ps
file
pdf
file
"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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file
pdf
file
"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
psfile
"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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file
pdf
file
"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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file
pdf
file
"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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file
pdf
file
"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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file
pdf
file
"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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file
Books
or parts of books
"Analysis of cell
centered finite volume methods for incompressible fluid flows",
Ecole de
Printemps de
Mécanique des Fluides Numérique,
Roscoff, Juin 2005.
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file
pdf
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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 intégration ", T.
Gallouët, R. Herbin, polycopié de
cours et
exercices corrigés de licence.
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"Cours
d'analyse numérique ",
R. Herbin, polycopié
de cours et exercices corrigés
de licence.
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pdf
file,
"Cours
d'analyse numérique des EDP ",
R. Herbin, polycopié
de cours et exercices corrigés de
master 1ère année.
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http://www.cmi.univ-mrs.fr/~herbin