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, Fabrie : Elements d'analyse pour l'étude de quelques modèles d'écoulements de fluides visqueux incompressibles, Coll. Mathématiques et Applications, vol.52, p.405, 2006.
, Mathematical study of multiphase flow under shear through order parameter formulation, Asymptotic Analysis, pp.175-212, 1999.
, Nonhomogeneous Cahn-Hilliard fluids, Annales de l'IHP : Analyse non linéaire, pp.225-259, 2001.
, A theoretical and numerical model for the study of incompressible mixture flows, Computers & Fluids, vol.31, issue.1, pp.41-68, 2002.
DOI : 10.1016/S0045-7930(00)00031-1
URL : https://hal.archives-ouvertes.fr/hal-00004084
, Fabrie : Persistency of 2D perturbations of 1D solutions for a Cahn-Hilliard flow model under high shear, Asymptotic Analysis, pp.107-151, 2003.
, Numerical study of viscoelastic mixtures through a Cahn???Hilliard flow model, European Journal of Mechanics - B/Fluids, vol.23, issue.5, pp.759-780, 2004.
DOI : 10.1016/j.euromechflu.2004.03.001
URL : https://hal.archives-ouvertes.fr/hal-00004087
, Finite volume schemes for the p-Laplacian on Cartesian meshes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.38, issue.6, pp.931-959, 2004.
DOI : 10.1051/m2an:2004045
URL : https://hal.archives-ouvertes.fr/hal-00004088
, Besov regularity and new error estimates for finite volume approximations of the p-laplacian, Numerische Mathematik, vol.3, issue.4, pp.565-592, 2005.
DOI : 10.1007/s00211-005-0591-8
URL : https://hal.archives-ouvertes.fr/hal-00004419
, Trace theorems and spatial continuity properties for the solutions of the transport equation, Differential and Integral Equations, pp.891-934, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00004420
, On the finite-volume approximation of regular solutions of the p-Laplacian, IMA Journal of Numerical Analysis, vol.26, issue.3, pp.472-502, 2006.
DOI : 10.1093/imanum/dri047
URL : https://hal.archives-ouvertes.fr/hal-00475905
, Discrete duality finite volume schemes for Leray-Lions type elliptic problems on general 2D meshes, Numerical Methods for PDEs, 2006.
, Study of a three component Cahn-Hilliard flow model, ESAIM: Mathematical Modelling and Numerical Analysis, vol.40, issue.4, 2006.
DOI : 10.1051/m2an:2006028
URL : https://hal.archives-ouvertes.fr/hal-00012276
, Discrete Besov framework for finite volume approximation of the plaplacian on non-uniform cartesian grids, ESAIM Proceedings, à paraître, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00475892
, Fabrie : Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations , Discerete and Continuous Dynamical Systems -Série B, à paraître, 2006.
, Finite volume methods for linear and nonlinear elliptic problems with discontinuities, soumis, 2006.
, Implicit definition of numerical fluxes for finite volume methods, en préparation, 2006.
, Finite volume approximation of an asymptotic model for flows in fractured porous media, en préparation, 2006.
, Ecoulements diphasiques de type Cahn-Hilliard, Thèse de Doctorat, 2001.
, Theoretical and numerical study of multiphase flows through order parameter formulation, EQUADIFF 99, International Conference on Differential Equations, pp.488-490, 1999.
, Duplex" finite-volume schemes for nonlinear elliptic problems on general 2D meshes, Finite Volumes for Complex Applications IV, Hermes Science, pp.365-376, 2005.
, Numerical modeling of flow in fractured porous media, Finite Volumes for Complex Applications IV, Hermes Science, pp.249-260, 2005.
, Lapuerta : A diffuse interface model for the numerical simulation of three-component flows, Finite Volumes for Complex Applications IV, Hermes Science, pp.153-162, 2005.
, Chupin : Etude numérique de mélanges visco-élastiques, Congrès d'Analyse Numérique, 2003.
, Angot : Un modèle de Navier-Stokes / Cahn-Hilliard pour la simulation d'écoulements incompressibles de trois phases non miscibles, 2005.
, An introduction to multipoint flux approximations for quadrilateral grids Locally conservative numerical methods for flow in porous media, Comput. Geosci, vol.6, pp.3-4405, 2002.
, Discretization on unstructured grids for inhomogeneous , anisotropic media. I. Derivation of the methods, SIAM J. Sci. Comput, vol.19, issue.5, pp.1700-1716, 1998.
, Discretization on unstructured grids for inhomogeneous , anisotropic media. II. Discussion and numerical results, SIAM J. Sci. Comput, vol.19, issue.5, pp.1717-1736, 1998.
, Traces and fine properties of a $BD$ class of vector fields and applications, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.14, issue.4, pp.527-561, 2005.
DOI : 10.5802/afst.1102
, Convergence of Finite Volume Approximations for a Nonlinear Elliptic-Parabolic Problem: A "Continuous" Approach, SIAM Journal on Numerical Analysis, vol.42, issue.1, pp.228-251227, 2004.
DOI : 10.1137/S0036142901400006
URL : https://hal.archives-ouvertes.fr/hal-00129680
, DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS, Annual Review of Fluid Mechanics, vol.30, issue.1, pp.139-165, 1998.
DOI : 10.1146/annurev.fluid.30.1.139
, Fractures and Fracture Networks, Kluwer Acad, vol.15, 1999.
DOI : 10.1007/978-94-017-1599-7
, Artificial boundary conditions for incompressible Navier-Stokes equations : a well-posed result, Comput. Methods Appl. Mech. Engrg, vol.188, issue.1-3, pp.595-611, 2000.
, Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels ; théorèmes d'approximation ; application à l'équation de transport, Ann. Sci. École Norm. Sup, vol.3, issue.4, pp.185-233, 1970.
, FINITE ELEMENT APPROXIMATION OF A MODEL FOR PHASE SEPARATION OF A MULTI-COMPONENT ALLOY WITH NONSMOOTH FREE ENERGY AND A CONCENTRATION DEPENDENT MOBILITY MATRIX, Mathematical Models and Methods in Applied Sciences, vol.09, issue.05, pp.627-663, 1999.
DOI : 10.1142/S0218202599000336
, À nouveau sur les équations de Stokes et de Navier- Stokes avec des conditions aux limites sur la pression, C. R. Acad. Sci. Paris Sér. I Math, vol.304, issue.1, pp.23-28, 1987.
, Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem, Journal of Mathematical Analysis and Applications, vol.336, issue.2, 2005.
DOI : 10.1016/j.jmaa.2007.03.024
URL : https://hal.archives-ouvertes.fr/hal-00017486
, Solution of the incompressible Navier-Stokes equations on domains with one or several open boundaries, Internat. J. Numer. Methods Fluids, issue.7, pp.311061-1085, 1999.
, Effective downstream boundary conditions for incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids, vol.59, issue.8, pp.693-705, 1994.
DOI : 10.1002/fld.1650190805
, New efficient boundary conditions for incompressible Navier-Stokes equations : a well-posedness result, ESAIM: Mathematical Modelling and Numerical Analysis, vol.30, issue.7, pp.815-840, 1996.
DOI : 10.1051/m2an/1996300708151
, AN ACCURATE FINITE DIFFERENCE SCHEME FOR SOLVING CONVECTION-DOMINATED DIFFUSION EQUATIONS, International Journal for Numerical Methods in Fluids, vol.88, issue.2, pp.169-183, 1997.
DOI : 10.1002/(SICI)1097-0363(19970130)24:2<169::AID-FLD486>3.0.CO;2-J
, Finite element approximation of the p-Laplacian, Math. Comp, issue.204, pp.61523-537, 1993.
, Effective permeability of fractured porous media in steady-state flow, Water Resour. Res, vol.107
, Boundary conditions on artificial frontiers for incompressible and compressible Navier- Stokes equations. M 2 AN Math, Model. Numer. Anal, vol.34, issue.2, pp.303-314, 2000.
, Théorèmes de trace L p pour des espaces de fonctions de la neutronique, C. R. Acad. Sci. Paris Sér. I Math, vol.299, issue.16, pp.831-834, 1984.
, Théorèmes de trace pour des espaces de fonctions de la neutronique, C. R. Acad. Sci. Paris Sér. I Math, vol.300, issue.3, pp.89-92, 1985.
, The Lions domain decomposition algorithm on non-matching cell-centred finite volume meshes, IMA Journal of Numerical Analysis, vol.24, issue.3, pp.465-490, 2004.
DOI : 10.1093/imanum/24.3.465
, Finite element error estimates for nonlinear elliptic equations of monotone type, Numer. Math, vol.54, issue.4, pp.373-393, 1989.
, Boundary layers for stress diffusive perturbation in viscoelastic fluids, Appl. Math. Lett, vol.18, issue.6, pp.641-647, 2005.
, The Stokes and Navier-Stokes equations with boundary conditions involving the pressure, Japan. J. Math. (N.S.), vol.20, issue.2, pp.279-318, 1994.
, Solving the fully coupled heart and torso problems of electrocardiology with a 3D discrete duality finite volume method. soumis, 2006.
, Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.3, pp.493-516, 1999.
DOI : 10.1051/m2an:1999149
, Discrete duality finite volume method for second order elliptic problems, Finite Volumes for Complex Applications IV, pp.447-358, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00868449
, On a nonlinear parabolic problem arising in some models related to turbulent flows, SIAM J. Math. Anal, vol.25, issue.4, pp.1085-1111, 1994.
, A mixed finite volume scheme for anisotropic diffusion problems on any grid. soumis, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00005565
, A few remarks on ordinary differential equations, Comm. Partial Differential Equations, vol.21, issue.1112, pp.1667-1703, 1996.
, Global existence results for the incompressible density-dependent Navier-Stokes equations in the whole space, Differential Integral Equations, vol.10, issue.3, pp.587-598, 1997.
, Linear transport equations with initial values in Sobolev spaces and application to the Navier-Stokes equations, Differential Integral Equations, vol.10, issue.3, pp.577-586, 1997.
, Ordinary differential equations, transport theory and Sobolev spaces, Inventiones Mathematicae, vol.307, issue.3, pp.511-547, 1989.
DOI : 10.1007/BF01393835
, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.6, pp.1203-1249, 2005.
DOI : 10.1051/m2an:2005047
, Finite volume approximations for fully non-linear elliptic equations in divergence form. soumis, 2005.
, Finite volume methods, VII, Handb. Numer. Anal., VII, pp.713-1020, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00346077
, A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension, IMA Journal of Numerical Analysis, vol.26, issue.2, pp.326-353, 2006.
DOI : 10.1093/imanum/dri036
, A control volume method to solve an elliptic equation on a two-dimensional irregular mesh, Comput. Methods Appl. Mech. Engrg, vol.100, issue.2, pp.275-290, 1992.
, A new fault model in geological basin modelling. Application of finite volume scheme and domain decomposition methods, Finite volumes for complex applications, III (Porquerolles, pp.529-536, 2002.
, Finite element approximation of nonlinear elliptic problems with discontinuous coefficients, ESAIM: Mathematical Modelling and Numerical Analysis, vol.24, issue.4, pp.457-500, 1990.
DOI : 10.1051/m2an/1990240404571
, Onset of entrainment between immiscible liquid layers due to rising gas bubbles, International Journal of Heat and Mass Transfer, vol.31, issue.6, pp.311309-1317, 1988.
DOI : 10.1016/0017-9310(88)90073-7
, Numerical methods for nonlinear variational problems. Springer Series in Computational Physics, 1984.
, Sur l'approximation, par ??l??ments finis d'ordre un, et la r??solution, par p??nalisation-dualit?? d'une classe de probl??mes de Dirichlet non lin??aires, Revue fran??aise d'automatique, informatique, recherche op??rationnelle. Analyse num??rique, vol.9, issue.R2, pp.41-76, 1975.
DOI : 10.1051/m2an/197509R200411
, On anisotropic order parameter models for multi-phase systems and their sharp interface limits, Physica D: Nonlinear Phenomena, vol.115, issue.1-2, pp.1-287, 1998.
DOI : 10.1016/S0167-2789(97)00227-3
, A MultiPhase Field Concept: Numerical Simulations of Moving Phase Boundaries and Multiple Junctions, SIAM Journal on Applied Mathematics, vol.60, issue.1, pp.295-315, 1999.
DOI : 10.1137/S0036139998334895
, Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology, ESAIM: Mathematical Modelling and Numerical Analysis, vol.37, issue.1, pp.175-186, 2003.
DOI : 10.1051/m2an:2003012
, A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comput. Phys, vol.160, issue.2, pp.481-499, 2000.
, Approximation of diffusion operators with discontinuous tensor coefficients on distorted meshes, Comput. Methods Appl. Mech. Engrg, vol.192, pp.16-181939, 2003.
, ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS, International Journal for Numerical Methods in Fluids, vol.8, issue.5, pp.325-352308, 1989.
DOI : 10.1002/(SICI)1097-0363(19960315)22:5<325::AID-FLD307>3.0.CO;2-Y
, Calculation of two-phase Navier-Stokes flows using phase-field modeling, Journal of Computational Physics, vol.155, pp.96-127, 1999.
, Contact-line dynamics of a diffuse fluid interface, Journal of Fluid Mechanics, vol.402, pp.57-88, 2000.
, Conservative multigrid methods for Cahn???Hilliard fluids, Journal of Computational Physics, vol.193, issue.2, pp.511-543, 2004.
DOI : 10.1016/j.jcp.2003.07.035
, Conservative multigrid methods for ternary Cahn-Hilliard systems, Commun. Math. Sci, vol.2, issue.1, pp.53-77, 2004.
, Phase field modeling and simulation of three-phase flows, Interfaces and Free Boundaries, vol.7, issue.4, pp.435-466, 2005.
DOI : 10.4171/IFB/132
, Well-posedness of the water-waves equations, Lap06] C. Lapuerta. Echanges de masse et de chaleur entre deux phases liquides stratifiées dans un écoulement à bulles, pp.605-654, 2005.
, A further remark on the regularity of the solutions of the p-Laplacian and its applications to their finite element approximation, Nonlinear Anal, vol.21, issue.5, pp.379-387, 1993.
, A remark on the regularity of the solutions of the p-Laplacian and its application to their finite element approximation, J. Math. Anal. Appl, vol.178, issue.2, pp.470-487, 1993.
, Transport equations with partially BV velocities, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.3, issue.54, pp.681-703, 2004.
, Mathematical topics in fluid mechanics, Tome 1 : Incompressible models, of Oxford Lecture Series in Mathematics and Applications, 1996.
, Degenerate quasilinear elliptic equations arising from bimaterial problems in elastic-plastic mechanics, Nonlinear Anal, vol.35, issue.4, pp.517-529, 1999.
, Finite element approximation of a nonlinear elliptic equation arising from bimaterial problems in elastic-plastic mechanics, Numer. Math, vol.86, issue.3, pp.491-506, 2000.
, Quelques résultats de Vi?ik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France, vol.93, pp.97-107, 1965.
, Schéma volumes finis monotone pour des opérateurs de diffusion fortement anisotropes sur des maillages de triangles non structurés, C. R. Math. Acad. Sci. Paris, issue.12, pp.341787-792, 2005.
, Schéma volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages non structurés, C. R. Math. Acad. Sci. Paris, issue.12, pp.340921-926, 2005.
, Quasi-incompressible Cahn-Hilliard fluids and topological transitions, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.454, issue.1978, pp.2617-2654, 1998.
DOI : 10.1098/rspa.1998.0273
, Uniform controllability of semidiscrete approximations of parabolic control systems, Systems & Control Letters, vol.55, issue.7, pp.597-609, 2006.
DOI : 10.1016/j.sysconle.2006.01.004
, On the trace problem for solutions of the Vlasov equation, Comm. Partial Differential Equations, vol.25, issue.78, pp.1415-1443, 2000.
, Modeling Fractures and Barriers as Interfaces for Flow in Porous Media, SIAM Journal on Scientific Computing, vol.26, issue.5, pp.1667-1691, 2005.
DOI : 10.1137/S1064827503429363
URL : https://hal.archives-ouvertes.fr/inria-00071735
, Rheological Response from Phase-Separated Domains as Studied by Shear Microscopy, Physical Review Letters, vol.80, issue.24, p.5441, 1998.
DOI : 10.1103/PhysRevLett.80.5441
, On extrapolation procedures at artificial outflow boundaries for the time-dependent Navier- Stokes equations, Appl. Numer. Math, vol.23, issue.4, pp.457-468, 1997.
, Nonlinear artificial boundary conditions with pointwise error estimates for the exterior three dimensional Navier-Stokes problem, Mathematische Nachrichten, vol.252, issue.1, pp.86-105, 2003.
DOI : 10.1002/mana.200310039
, Nonlinear artificial boundary conditions for the Navier-Stokes equations in an aperture domain, Mathematische Nachrichten, vol.265, issue.1, pp.24-67, 2004.
DOI : 10.1002/mana.200310135
, PELICANS : Un outil d'implémentation de solveurs d'équations aux dérivées partielles. Note Technique, 2004.
, Modélisation et simulation de l'activité électrique du coeur dans le thorax, analyse numérique et méthodes de volumes finis, 2005.
, Numerical simulation of the motion of a two-dimensional glacier, International Journal for Numerical Methods in Engineering, vol.60, issue.5, pp.995-1009, 2004.
DOI : 10.1002/nme.997
, Caractérisation d'espaces fonctionnels Régularité de la solution d'un problème aux limites non linéaires, Boll. Un. Mat. Ital. B Ann. Fac. Sci. Toulouse Math, vol.15, issue.3, pp.687-7143, 1978.
, Nonhomogeneous viscous incompressible fluids : existence of velocity, density, and pressure
, A projection method for motion of triple junctions by level sets. Interfaces and Free Boundaries, pp.239-261, 2002.
, Artificial boundary conditions for the linearized compressible Navier-Stokes equations, J. Comput. Phys, vol.137, issue.1, pp.1-37, 1997.
, Artificial boundary conditions for the linearized compressible Navier-Stokes equations. II. The discrete approach, J. Comput. Phys, vol.144, issue.1, pp.151-179, 1998.
, A diffuse-interface method for simulating two-phase flows of complex fluids, Journal of Fluid Mechanics, vol.515, pp.293-317, 2004.
DOI : 10.1017/S0022112004000370
, The finite element method for nonlinear elliptic equations with discontinuous coefficients, Numer. Math, vol.58, issue.1, pp.51-77, 1990.