Publications plus anciennes - older publications

Paul Corbel (1957-2019), un humaniste au service de l'industrie


[12] F. Bouchut, D. Doyen, and R. Eymard.
Convection and total variation flow–erratum and improvement.
IMA J. Numer. Anal., 37(4):2139–2169, 2017.


[13] C. Cocozza-Thivent, R. Eymard, L. Goudenège, and M. Roussignol.
Numerical methods for piecewise deterministic Markov processes with boundary.
IMA Journal of Numerical Analysis, 37(1):170–208, 2017.


[14] P. Deuring and R. Eymard.
L2-stability of a finite element – finite volume discretization of convection-diffusion-reaction equations with nonhomogeneous mixed boundary conditions.
ESAIM: M2AN, 51(3):919–947, 2017.


[15] J. Droniou and R. Eymard.
Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations.
Numerische Mathematik, 132(4):721–766, 2016.


[16] J. Droniou, R. Eymard, and P. Feron.
Gradient Schemes for Stokes problem.
IMA Journal of Numerical Analysis, 36(4):1636–1669, 2016.


[17] J. Droniou, R. Eymard, and R. Herbin.
Gradient schemes: generic tools for the numerical analysis of diffusion equations .
ESAIM: M2AN, 50(3):749–781, 2016.


[18] J. Droniou, R. Eymard, and K. S. Talbot.
Convergence in C([0,T];L2(Omega)) of weak solutions to perturbed doubly degenerate parabolic equations.
Journal of Differential Equations, 260(11):7821–7860, 2016.


[19] E. Chénier, R. Eymard, T. Gallouet, and R. Herbin.
An extension of the MAC scheme to locally refined meshes : convergence analysis for the full tensor time-dependent Navier-Stokes equations.
Calcolo, 52:69–107, 2015.


[20] P. Deuring, R. Eymard, and M. Mildner.
L2-stability independent of diffusion for a finite element – finite volume discretization of a linear convection-diffusion equation.
Siam J. Numer. Anal., 53(1):508–526, 2015.


[21] R. Eymard, T. Gallouët, and R. Herbin.
RTk mixed finite elements for some nonlinear problems.
Mathematics and Computers in Simulation, 118:186–197, 2015.


[22] R. Eymard, A. Handlovicova, R. Herbin, K. Mikula, and O. Stašová.
Applications of approximate gradient schemes for nonlinear parabolic equations.
Applications of Mathematics, 60(2):135–156, 2015.


[23] P. Gunawan, R. Eymard, and S. Pudjaprasetya.
Staggered scheme for the Exner–shallow water equations.
Computational Geosciences, 19(6):1197–1206, 2015.


[24] F. Bouchut, D. Doyen, and R. Eymard.
Convection and total variation flow.
IMA J. Numer. Anal., 34(3):1037–1071, 2014.


[25] F. Bouchut, R. Eymard, and A. Prignet.
Convergence of conforming approximations for inviscid incompressible Bingham fluid flows and related problems.
Journal of Evolution Equations, 14(3):635–669, 2014.


[26] R. Eymard, J. Fuhrmann, and A. Linke.
On MAC Schemes on Triangular Delaunay Meshes, their Convergence and Application to Coupled Flow Problems.
Numerical Methods for Partial Differential Equations, 30(4):1397–1424, 2014.


[27] R. Eymard, T. Gallouet, C. Guichard, R. Herbin, and R. Masson.
TP or not TP, that is the question.
Comp. Geosciences, 18:285–296, 2014.


[28] R. Eymard, C. Guichard, R. Herbin, and R. Masson.
Gradient schemes for two-phase flow in heterogeneous porous media and Richards equation.
ZAMM - J. of App. Math. and Mech., 94(7-8):560–585, 2014.


[29] R. Eymard and V. Schleper.
Study of a numerical scheme for miscible two-phase flow in porous media.
Numer. Methods Partial Differential Equations, 30(3):723–748, 2014.


[30] B. Andreianov, R. Eymard, M. Ghilani, and N. Marhraoui.
Finite volume approximation of degenerate two-phase flow model with unlimited air mobility.
Numer. Methods Partial Differential Equations, 29(2):441–474, 2013.


[31] G. Desrayaud, E. Chénier, A. Joulin, A. Bastide, B. Brangeon, J. Caltagirone, Y. Cherif, R. Eymard, C. Garnier, S. Giroux-Julien, Y. Harmane, P. Joubert, N. Laaroussi, S. Lassue, P. Le Quere, R. Li, D. Saury, A. Sergent, S. Xin, and A. Zoubir.
Benchmark solutions for natural convection flows in vertical channels submitted to different open boundary conditions.
International Journal of Thermal Sciences, 72:18–33, 2013.


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


[33] R. Eymard, P. Féron, T. Gallouet, R. Herbin, and C. Guichard.
Gradient schemes for the Stefan problem.
Int. J. Finite Vol., 10, 2013.


[34] R. Eymard, C. Guichard, and R. Masson.
Grid Orientation Effect in coupled Finite Volume Schemes.
IMA J. Numer. Anal., 33(2):582–608, 2013.


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


[36] R. Eymard, C. Guichard, and R. Herbin.
Small-stencil 3D schemes for diffusive flows in porous media.
M2AN, 46:265–290, 2012.


[37] R. Eymard, A. Handlovičová, and K. Mikula.
Approximation of nonlinear parabolic equations using a family of conformal and non-conformal schemes.
Communications on Pure and Applied Analysis, 11(1):147–172, 2012.


[38] R. Eymard, M. Henry, and D. Hilhorst.
Singular limit of a two-phase flow problem in porous medium as the air viscosity tends to zero.
Discrete and Continuous Dynamical Systems - Series S, 5(1):93–113, 2012.


[39] R. Eymard, R. Herbin, C. Guichard, and R. Masson.
Vertex Centred Discretization of Multiphase Compositional Darcy Flows on General Meshes.
Comput. Geosc., 16(4):987–1005, 2012.


[40] R. Eymard, R. Herbin, C. Guichard, and R. Masson.
Vertex Centred Discretization of Two Phase Flows on General Meshes.
ESAIM: Proc., 35:59–78, 2012.


[41] R. Eymard, M. Roussignol, and A. Tordeux.
Convergence of a misanthrope process to the entropy solution of 1D problems.
Stochastic Processes and their Applications, 122:3648–3679, 2012.


[42] O. Angelini, C. Chavant, E. Chénier, R. Eymard, and S. Granet.
Finite volume approximation of a diffusion-dissolution model and application to nuclear waste storage.
Mathematics and Computers in Simulation, 81(10):2001–2017, 2011.


[43] F. Bouchut, R. Eymard, and A. Prignet.
Finite volume schemes for the approximation via characteristics of linear convection equations with irregular data.
Journal of Evol. Eq., 11(3):687–724, 2011.


[44] R. Eymard, A. Handlovičová, and K. Mikula.
Study of a finite volume scheme for the regularized mean curvature flow level set equation.
IMA J. Numer. Anal., 31(3):813–846, 2011.


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


[46] R. Eymard, S. Mercier, and M. Roussignol.
Importance and sensitivity analysis in dynamic reliability.
Methodol. Comput. Appl. Probab., 13(1):75–104, 2011.


[47] L. Agélas, D. A. Di Pietro, R. Eymard, and R. Masson.
An abstract analysis framework for nonconforming approximations of diffusion problems on general meshes.
Int. J. Finite Vol., 7(1):1–29, 2010.


[48] O. Angelini, C. Chavant, E. Chénier, and R. Eymard.
A finite volume scheme for diffusion problems on general meshes applying monotony constraints.
SIAM J. Numer. Anal., 47(6):4193–4213, 2010.


[49] J. Droniou, R. Eymard, T. Gallouët, and R. Herbin.
A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods.
Math. Models Methods Appl. Sci., 20(2):265–295, 2010.


[50] R. Eymard, T. Gallouët, and R. Herbin.
Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces.
IMA Journal of Numerical Analysis, 30(4):1009–1043, 2010.


[51] R. Eymard, T. Gallouët, R. Herbin, and J. C. Latché.
A convergent finite element-finite volume scheme for the compressible Stokes problem. II. The isentropic case.
Math. Comp., 79(270):649–675, 2010.


[52] R. Eymard, T. Gallouët, R. Herbin, and J.-C. Latché.
Convergence of the MAC Scheme for the Compressible Stokes Equations.
SIAM Journal on Numerical Analysis, 48(6):2218–2246, 2010.


[53] R. Eymard and R. Herbin.
Approximation of the biharmonic problem using piecewise linear finite elements.
C. R. Math. Acad. Sci. Paris, 348(23-24):1283–1286, 2010.


[54] R. Eymard, D. Hilhorst, H. Murakawa, and M. Olech.
Numerical approximation of a reaction-diffusion system with fast reversible reaction.
Chinese Annals of Mathematics - Series B, 31:631–654, 2010.
10.1007/s11401-010-0604-5.


[55] R. Eymard, D. Hilhorst, and M. Vohralík.
A combined finite volume-finite element scheme for the discretization of strongly nonlinear convection-diffusion-reaction problems on nonmatching grids..
Numer. Methods Partial Differ. Equations, 26(3):612–646, 2010.


[56] L. Agélas, R. Eymard, and R. Herbin.
A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media.
C. R. Acad. Sci. Paris, 347(11–12):673–676, 2009.


[57] N. Bouillard, R. Eymard, M. Henry, R. Herbin, and D. Hilhorst.
A fast precipitation and dissolution reaction for a reaction-diffusion system arising in a porous medium.
Nonlinear Analysis: Real World Applications, 10(2):629–638, 2009.


[58] E. Chénier, R. Eymard, and R. Herbin.
A collocated finite volume scheme to solve free convection for general non-conforming grids.
Journal of Computational Physics, 228(6):2296–2311, 2009.


[59] J. Droniou and R. Eymard.
Study of the mixed finite volume method for Stokes and Navier-Stokes equations.
Numerical Methods for Partial Differential Equations, 25(1):137–171, 2009.


[60] R. Eymard, T. Gallouët, and R. Herbin.
Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral grids.
J. Numer. Math., 17(3):173–193, 2009.


[61] R. Eymard, R. Herbin, J. Latché, and B. Piar.
Convergence analysis of a locally stabilized collocated finite volume scheme for incompressible flows.
ESAIM: M2AN, 43(5):889–927, 2009.


[62] E. Chénier, R. Eymard, R. Herbin, and O. Touazi.
Collocated finite volume schemes for the simulation of natural convective flows on unstructured meshes.
International Journal for Numerical Methods in Fluids, 56(11):2045–2068, 2008.


[63] E. Chénier, R. Eymard, and O. Touazi.
Simulation of natural convection with the collocated clustered finite volume scheme.
Computers and Fluids, 37(9):1138–1147, 2008.


[64] F. Daım, R. Eymard, D. Hilhorst, and J. Laminie.
Algorithms for coupled mechanical deformations and fluid flow in a porous medium with different time scales.
International Journal of Numerical Analysis and Modeling, 5(4):635–658, 2008.


[65] R. Eymard and S. Mercier.
Comparison of numerical methods for the assessment of production availability of a hybrid system.
Reliability Engineering & System Safety, 93(1):169–178, 2008.


[66] R. Eymard, S. Mercier, and A. Prignet.
An implicit finite volume scheme for a scalar hyperbolic problem with measure data related to piecewise deterministic Markov processes.
Journal of Computational and Applied Mathematics, 222(2):293–323, 2008.


[67] S. Gholamifard, R. Eymard, and C. Duquennoi.
Modeling anaerobic bioreactor landfills in methanogenic phase: Long term and short term behaviors.
Water Research, 42(20):5061–5071, 2008.


[68] N. Bouillard, R. Eymard, R. Herbin, and Ph. Montarnal.
Diffusion with dissolution and precipitation in a porous media: Mathematical analysis and numerical approximation of a simplified model.
ESAIM: M2AN, 41(6):975–1000, 2007.


[69] F. Daim, R. Eymard, and D. Hilhorst.
Existence of a solution for two phase flow in porous media : the case that the porosity depends on the pressure.
Journal of Mathematical Analysis and Applications, 326(1):332–351, 2007.


[70] R. Eymard and T. Gallouët.
A Partial Differential Inequality in Geological Models.
Chinese Ann. of Math. Ser.B., 28(6):709–736, 2007.


[71] R. Eymard, T. Gallouët, and R. Herbin.
Finite volume schemes for nonlinear parabolic problems: another regularization method.
Acta Math. Univ. Comen., New Ser., 76(1):3–10, 2007.


[72] R. Eymard, T. Gallouët, and R. Herbin.
A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis.
Comptes rendus Mathématiques de l'Académie des Sciences, 344(6):403–406, 2007.


[73] R. Eymard, T. Gallouët, R. Herbin, and J.-C. Latché.
Analysis tools for finite volume schemes.
Acta Math. Univ. Comen., New Ser., 76(1):111–136, 2007.


[74] R. Eymard and R. Herbin.
A new colocated finite volume scheme for the incompressible Navier-Stokes equations on general non matching grids.
Comptes rendus Mathématiques de l'Académie des Sciences, 344(10):659–662, 2007.


[75] R. Eymard, R. Herbin, and J. C. Latché.
Convergence Analysis of a Colocated Finite Volume Scheme for the Incompressible Navier–Stokes Equations on General 2D or 3D Meshes .
SIAM Journal on Numerical Analysis, 45(1):1–36, 2007.


[76] R. Eymard, R. Herbin, J.C. Latché, and B. Piar.
On the stability of colocated clustered finite volume simplicial discretizations for the 2D Stokes problem.
Calcolo, 44(4):219–234, 2007.


[77] R. Eymard and E. Tillier.
Mathematical and Numerical Study of a System of Conservation Laws.
J. of Evolution Equations, 7(2):197–239, 2007.


[78] J. Berton and R. Eymard.
Finite volume methods for the valuation of american options.
ESAIM: M2AN, 40(2):311–330, 2006.


[79] J. Blum, G. Dobranszky, R. Eymard, and R. Masson.
Inversion of a stratigraphic model to fit seismic data.
Inverse Problems, 22:1207–1225, 2006.


[80] E. Chénier, R. Eymard, and O. Touazi.
Numerical results using a colocated finite-volume scheme on unstructured grids for incompressible fluid flows.
Numerical heat transfer. Part B, fundamentals, 49(3):259–276, 2006.


[81] C. Cocozza-Thivent, R. Eymard, and S. Mercier.
A finite-volume scheme for dynamic reliability models.
IMA J. Numer. Anal., 26(3):446–471, 2006.


[82] Christiane Cocozza-Thivent, Robert Eymard, Sophie Mercier, and Michel Roussignol.
Characterization of the marginal distributions of markov processes used in dynamic reliability.
Journal of Applied Mathematics and Stochastic Analysis, 2006:Article ID 92156, 18 pages, 2006.


[83] J. Droniou and R. Eymard.
A mixed finite volume scheme for anisotropic diffusion problems on any grid.
Numerische Mathematik, 105(1):35–71, 2006.


[84] Guillaume Enchéry, R. Eymard, and A. Michel.
Numerical approximation of a two-phase flow problem in a porous medium with discontinuous capillary forces.
SIAM J. Numer. Anal., 43(6):2402–2422 (electronic), 2006.


[85] R. Eymard and T. Gallouët.
Analytical and numerical study of a model of erosion and sedimentation.
SIAM J. on Num. Anal., 43(6):2344–2370„ 2006.


[86] R. Eymard, T. Gallouët, and R. Herbin.
A cell-centered finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension.
IMA J. Numer. Anal., 26(2):326–353, 2006.


[87] R. Eymard, R. Herbin, and J.C. Latché.
On a stabilized colocated Finite Volume scheme for the Stokes problem.
ESAIM: M2AN, 40(3):501–527, 2006.


[88] R. Eymard, D. Hilhorst, and Vohralık.
A combined finite volume nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems.
Numerische Mathematik, 105(1):73–131, 2006.


[89] J. Bénard, R. Eymard, X. Nicolas, and C. Chavant.
Boiling in porous media : Model and Simulations.
Transp. Porous Media, 60:1–31, 2005.


[90] P. Blanc, R. Eymard, and R. Herbin.
A staggered finite volume scheme, part i.
Int. J. on Finite Volumes, 2005.


[91] R. Eymard, J. Fuhrmann, and K. Gärtner.
A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local Dirichlet problems.
Numerische Mathematik (Published online: 13 December 2005), 102(3):463–495, 2006.


[92] R. Eymard, T. Gallouët, V. Gervais, and R. Masson.
Convergence of a numerical scheme for stratigraphic modeling.
SIAM J. Numer. Anal., 43(2):474–501 (electronic), 2005.


[93] R. Eymard and R. Herbin.
A staggered finite volume scheme, part ii.
Int. J. on Finite Volumes, 2005.


[94] P. Blanc, R. Eymard, and R. Herbin.
An error estimate for finite volume methods for the stokes equations on equilateral triangular meshes.
Numer. Methods Partial Differential Equations, 20(6):907–918, 2004.


[95] E. Chénier, R. Eymard, and X. Nicolas.
A finite volume scheme for the transport of radionucleides in porous media.
Comput. Geosci., 8(2):163–172, 2004.


[96] C. Cocozza-Thivent and R. Eymard.
Approximation of the marginal distributions of a semi-markov process using a finite volume scheme.
ESAIM: M2AN, 38:853–875, 2004.


[97] R. Eymard and T. Gallouët.
Finite volume schemes for two-phase flow in porous media.
Comput. Visual. Sci., 7:31–40, 2004.


[98] R. Eymard, T. Gallouët, D. Granjeon, R. Masson, and Q. H. Tran.
Multi-lithology stratigraphic model under maximum erosion rate constraint.
Internat. J. Numer. Methods Engrg., 60(2):527–548, 2004.


[99] R. Eymard, T. Gallouët, and R. Herbin.
A finite volume scheme for anisotropic diffusion problems.
Comptes Rendus de l'Académie des Sciences, 339(4):299–302, 2004.


[100] O. Coussy and R. Eymard.
Non-linear binding and the diffusion-migration test.
Transport in Porous Media, 53(1):51–74, 2003.


[101] J. Droniou, R. Eymard, D. Hilhorst, and X. D. Zhou.
Convergence of a finite-volume mixed finite-element method for an elliptic-hyperbolic system.
IMA J. Numer. Anal., 23(3):507–538, 2003.


[102] R. Eymard and T. Gallouët.
H-convergence and numerical schemes for elliptic equations.
SIAM Journal on Numerical Analysis, 41(2):539–562, 2003.


[103] R. Eymard, T. Gallouët, and J. Vovelle.
Limit boundary conditions for finite volume approximations of some physical problems.
Journal of Computational and Applied Mathematics, 161:349–369, 2003.


[104] R. Eymard and R. Herbin.
A cell-centered finite volume scheme on general meshes for the stokes equations in two space dimensions.
C. R. Math. Acad. Sci. Paris, 337(2):125–128, 2003.


[105] R. Eymard, R. Herbin, and A. Michel.
Mathematical study of a petroleum-engineering scheme.
ESAIM : M2AN, 37:937–972, 2003.


[106] F. Daim, R. Eymard, M. Mainguy, R. Masson, and D. Hilhorst.
A preconditioned conjugate gradient based algorithm for coupling.
Oil Gas Science and Technology, 57(5):515–523, 2002.


[107] G. Enchéry, R. Masson, S. Wolf, and R. Eymard.
Mathematical and numerical study of an industrial scheme for two-phase flows in porous media under gravity.
Comput. Methods Appl. Math., 2(4):325–353, 2002.


[108] R. Eymard, T. Gallouët, and R. Herbin.
Error estimate for approximate solutions of a nonlinear convection-diffusion problem.
Advances in Differential Equations, 7(4):419–440, 2002.


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


[110] R. Eymard, T. Gallouët, and R. Herbin.
Finite volume approximation of elliptic problems and convergence of an approximate gradient.
Appl. Numer. Math., 37(1-2):31–53, 2001.


[111] R. Eymard, T. Gallouët, R. Herbin, M. Gutnic, and D. Hilhorst.
Approximation by the finite volume method of an elliptic-parabolic equation arising in environmental studies.
Math. Models Methods Appl. Sci., 11(9):1505–1528, 2001.


[112] R. Eymard, D. Hilhorst, L.A. Peletier, and R. van der Hout.
A reaction-diffusion system approximation of a one-phase stefan problem.
Menaldi, José Luis (ed.) et al., Optimal control and partial differential equations. In honour of Professor Alain Bensoussan's 60th birthday. Proceedings of the conference, pages 156–170, 2001.


[113] R. Eymard, T. Gallouët, and R. Herbin.
Convergence of finite volume schemes for semilinear convection diffusion equations.
Num. Math., 82:91–116, 1999.


[114] R. Eymard, T. Gallouët, R. Herbin, D. Hilhorst, and M. Mainguy.
Instantaneous and noninstantaneous dissolution: approximation by the finite volume method.
In Actes du 30ème Congrès d'Analyse Numérique: CANum '98 (Arles, 1998), volume 6 of ESAIM Proc., pages 41–55 (electronic). Soc. Math. Appl. Indust., Paris, 1999.


[115] Robert Eymard, Michaël Gutnic, and Danielle Hilhorst.
The finite volume method for Richards equation.
Comput. Geosci., 3(3-4):259–294, 1999.


[116] O. Coussy, P. Dangla, and R. Eymard.
A vanishing diffusion process in unsaturated soils.
Int. J. Non-Linear Mechanics, 33(6):1027–1037, 1998.


[117] O. Coussy, R. Eymard, and T. Lassabatère.
Constitutive modeling of unsaturated drying deformable materials.
Journal of engineering mechanics, 124(6), 1998.


[118] R. Eymard, T. Gallouët, M. Ghilani, and R. Herbin.
Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes.
IMA J. Numer. Anal., 18(4):563–594, 1998.


[119] R. Eymard, T. Gallouët, D. Hilhorst, and Y. Naıt Slimane.
Finite volumes and nonlinear diffusion equations.
RAIRO Modél. Math. Anal. Numér., 32(6):747–761, 1998.


[120] R. Eymard, M. Gutnic, and D. Hilhorst.
The finite volume method for an elliptic-parabolic equation.
Acta Math. Univ. Comen., New Ser., 67(1):181–195, 1998.


[121] R. Eymard, T. Gallouët, and R. Herbin.
Existence and uniqueness of the entropy solution to a nonlinear hyperbolic equation.
Chinese Ann. Math. Ser. B, 16(1):1–14, 1995.
A Chinese summary appears in Chinese Ann. Math. Ser. A 16 (1995), no. 1, 119.