# Robert EYMARD

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 Nom: EYMARD Prénom: Robert Site: UGE Bureau: 4B 011 Téléphone: +33 1 60 95 72 81 Situation: Permanent Statut: Professeur Équipe de recherche: Équations aux dérivées partielles Courriel: robert.eymard [at] univ-eiffel.fr Page personnelle: http://perso.math.u-pem.fr/eymard.robert/

## Publications au sein du laboratoire

La liste ci-dessous présente les publications du membre obtenues pendant sa présence au sein du laboratoire. Les données proviennent des serveurs de HAL ; il peut donc y avoir des oublis, des doublons ou des erreurs.

Computational Methods in Applied Mathematics (2019)
Springer International Publishing AG Mathématiques et Applications 82 (2018)
• Unified convergence analysis of numerical schemes for a miscible displacement problem
Foundations of Computational Mathematics (2018)
• An error estimate for the approximation of linear parabolic equations by the Gradient Discretization Method
FVCA 2017 - International Conference on Finite Volumes for Complex Applications VIII (2017)
• DGM, an item of GDM
FVCA 2017 - International Conference on Finite Volumes for Complex Applications VIII (2017)
• Discontinuous Galerkin gradient discretisations for the approximation of second-order differential operators in divergence form
Computational and Applied Mathematics (2017)
• Numerical methods for piecewise deterministic Markov processes with boundary
IMA Journal of Numerical Analysis 37 1 (2017) 170-208
• Family of convergent numerical schemes for the incompressible Navier-Stokes equations
Mathematics and Computers in Simulation (2017)
• Gradient schemes: generic tools for the numerical analysis of diffusion equations
ESAIM: Mathematical Modelling and Numerical Analysis 50 3 (2016) 749-781
• Convergence in $C(\lbrack0,T\rbrack;L^2(\Omega))$ of weak solutions to perturbed doubly degenerate parabolic equations
Journal of Differential Equations (2016)
• Applications of approximate gradient schemes for nonlinear parabolic equations
Applications of Mathematics (2015)
MAMERN VI–2015: 6 th International Conference on Approximation Methods and Numerical Modelling in Environment and Natural Resources (2015)
• Uniform-in-time convergence result of numerical methods for non-linear parabolic equations
Numerische Mathematik (2015)
• Gradient Schemes for Stokes problem
IMA Journal of Numerical Analysis (2015)
• L2-stability independent of diffusion for a finite element -- finite volume discretization of a linear convection-diffusion equation
SIAM Journal on Numerical Analysis (2015)
• TP or not TP, that is the question
Computational Geosciences (2014) 18:285-296, 2014
• An extension of the MAC scheme to locally refined meshes : convergence analysis for the full tensor time-dependent Navier-Stokes equations
Calcolo 52 1 (2014) 69-107
• Convection and total variation flow
IMA Journal of Numerical Analysis (2014)
• High Performance Computing linear algorithms for two-phase flow in porous media
FVCA7 - The International Symposium of Finite Volumes for Complex Applications VII (2014)
• Uniform-in-time convergence of numerical schemes for Richards' and Stefan's models
FVCA7 - The International Symposium of Finite Volumes for Complex Applications VII (2014)
• Convergence of conforming approximations for inviscid incompressible Bingham fluid flows and related problems
Journal of Evolution Equations (2014) 14(3):635-669, 2014
• Gradient schemes: a generic framework for the discretisation of linear, nonlinear and nonlocal elliptic and parabolic equations
Mathematical Models and Methods in Applied Sciences (2013) 23(13), 2395-2432
• Gradient schemes for the Stefan problem
International Journal on Finite Volumes (2013) Volume 10 special
• Study of a numerical scheme for miscible two-phase flow in porous media
Numerical Methods for Partial Differential Equations (2013) 30(3):723-748, 2014
• Gradient schemes for two-phase flow in heterogeneous porous media and Richards equation
Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (2013) Volume 94, Issue 7-8, pages 560–585, July 2014
• Approximation of nonlinear parabolic equations using a family of conformal and non-conformal schemes
Communications on Pure and Applied Mathematics 11 1 (2012) http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=6484
• Vertex-centred discretization of multiphase compositional Darcy flows on general meshes
Computational Geosciences 16 4 (2012) 987 - 1005
• Grid Orientation Effect in coupled Finite Volume Schemes
IMA Journal of Numerical Analysis (2012) http://imajna.oxfordjournals.org/cgi/authordata?d=10.1093/imanum/drs016&k=929ef8d7
• Finite volume approximation of degenerate two-phase flow model with unlimited air mobility
Numerical Methods for Partial Differential Equations 29 2 (2012) pp. 441-474
• Finite volume schemes for the biharmonic problem on general meshes
Mathematics of Computation 81 280 (2012) 2019-2048
• Small-stencil 3D schemes for diffusive flows in porous media
ESAIM: Mathematical Modelling and Numerical Analysis 46 (2012) 265-290
• Convergence of a misanthrope process to the entropy solution of 1D problems
Stochastic Processes and their Applications 122 (2012) http://www.sciencedirect.com/science/article/pii/S0304414912001536
• Vertex centred Discretization of Two-Phase Darcy flows on General Meshes
ESAIM: Proceedings 35 (2012) 59-78
• Importance and Sensitivity Analysis in Dynamic Reliability
Methodology and Computing in Applied Probability 13 1 (2011) 75-104
• Study of a finite volume scheme for the regularised mean curvature flow level set equation
IMA Journal of Numerical Analysis (2011) http://imajna.oxfordjournals.org/content/31/3/813
• Finite volume schemes for the approximation via characteristics of linear convection equations with irregular data
Journal of Evolution Equations 11 3 (2011) 687-724
• An Extension of the MAC Scheme to some Unstructured Meshes
6th International Symposium on Finite Volumes for Complex Applications 4 (2011) 253-261
• 3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids
Finite Volume for Complex Applications VI (2011) 895--930
• Finite volume approximation of a diffusion-dissolution model and application to nuclear waste storage
Mathematics and Computers in Simulation 81 10 (2011) 2001-2017
• Approximation of the biharmonic problem using P1 finite elements
Journal of Numerical Mathematics (2011) Volume 19, Issue 1, Pages 1-26
• Hybrid finite volume discretization of linear elasticity models on general meshes
Finite Volumes for Complex Applications VI Problems & Perspectives 4 (2011) 331-339
• On Intrinsic Formulation and Well-posedness of a Singular Limit of Two-phase Flow Equations in Porous Media
Eleventh International Conference Zaragoza–Pau on Applied Mathematics and Statistics 38 (2010) pp. 21-34
• An abstract analysis framework for nonconforming approximations of diffusion problems on general meshes
International Journal on Finite Volumes 7 1 (2010) 1-29
• Approximation of the biharmonic problem using piecewise linear finite elements,Approximation d'un problème biharmonique par élément fini P1
Comptes Rendus Mathématique 348 (2010) 1283-1286
• A Collocated Finite Volume Scheme for the Incompressible Navier-Stokes Equations on General Non-Matching Grids
5th International Symposium on Finite Volumes for Complex Applications (2010) 289-296
• Convergence of the MAC scheme for the compressible Stokes equations
SIAM Journal on Numerical Analysis 48 6 (2010) 2218-2246
• A combined finite volume-finite element scheme for the discretization of strongly nonlinear convection-diffusion-reaction problems on nonmatching grids
Numerical Methods for Partial Differential Equations 26 3 (2009) 612-646
• Convergence analysis of a locally stabilized collocated finite volume scheme for incompressible flows
ESAIM: Mathematical Modelling and Numerical Analysis 43 5 (2009) 889-927
• 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 (2009) 635-658
• 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 (2009) 635-658
• Towards a generalization of the MAC scheme on unstructured meshes
Workshop on Discretization methods for viscous flows (2009)
• Study of the mixed finite volume method for Stokes and Navier-Stokes equations
Numerical Methods for Partial Differential Equations (2008)
• Comparison of numerical methods for the assessment of production availability of a hybrid system
Reliability Engineering and System Safety 93 1 (2008) 168-177
• 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 (2008) 293-323
• 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 (2007) 332-351
• Mathematical and numerical study of a system of conservation laws
Journal of Evolution Equations (2007) http://www.springerlink.com/content/wrj46l34231r8k66/?MUD=MP
• A mixed finite volume scheme for anisotropic diffusion problems on any grid
Numerische Mathematik 105 (2006) http://rd.springer.com/article/10.1007/s00211-006-0034-1
• Characterization of the marginal distributions of Markov processes used in dynamic reliability
Journal of Applied Mathematics and Stochastic Analysis 2006 (2006) 1-18
• On a stabilized colocated Finite Volume scheme for the Stokes problem
ESAIM: Mathematical Modelling and Numerical Analysis 40 3 (2006) 501-527
• Identification of a stratigraphic model with seismic constraints
Inverse Problems 22 (2006) 1207-1225
• A finite-volume scheme for dynamic reliability models
IMA Journal of Numerical Analysis 26 3 (2005) 446-471
• Finite volume schemes for two phase flow in porous media
Computing and Visualization in Science 7 (2004) 31-40
• A finite volume scheme for anisotropic diffusion problems
Comptes rendus de l'Académie des sciences. Série I, Mathématique (2004) 299-302
• Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme
ESAIM: Mathematical Modelling and Numerical Analysis 38 5 (2004) 853-875
• Limit boundary conditions for finite volume approximations of some physical problems
Journal of Computational and Applied Mathematics (2003) pp. 349-369
• H-convergence and numerical schemes for elliptic equations
SIAM Journal on Numerical Analysis (2003) 539-562
Laboratoire d'Analyse et de Mathématiques Appliquées
Université Gustave Eiffel
5 boulevard Descartes
Bâtiment Copernic
77420 Champs-sur-Marne