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Bibliography

Major publications by the team in recent years
  • 1C. Bataillon, F. Bouchon, C. Chainais-Hillairet, C. Desgranges, E. Hoarau, F. Martin, S. Perrin, M. Tupin, J. Talandier.

    Corrosion modelling of iron based alloy in nuclear waste repository, in: Electrochim. Acta, 2010, vol. 55, no 15, pp. 4451–4467.
  • 2C. Bataillon, F. Bouchon, C. Chainais-Hillairet, J. Fuhrmann, E. Hoarau, R. Touzani.

    Numerical methods for the simulation of a corrosion model with moving oxide layer, in: J. Comput. Phys., 2012, vol. 231, no 18, pp. 6213–6231.

    http://dx.doi.org/10.1016/j.jcp.2012.06.005
  • 3M. Bessemoulin-Chatard, C. Chainais-Hillairet, M.-H. Vignal.

    Study of a fully implicit scheme for the drift-diffusion system. Asymptotic behavior in the quasi-neutral limit., in: SIAM, J. Numer. Anal., 2014, vol. 52, no 4.

    http://epubs.siam.org/toc/sjnaam/52/4
  • 4C. Calgaro, E. Chane-Kane, E. Creusé, T. Goudon.

    L∞-stability of vertex-based MUSCL finite volume schemes on unstructured grids: simulation of incompressible flows with high density ratios, in: J. Comput. Phys., 2010, vol. 229, no 17, pp. 6027–6046.
  • 5C. Calgaro, E. Creusé, T. Goudon.

    An hybrid finite volume-finite element method for variable density incompressible flows, in: J. Comput. Phys., 2008, vol. 227, no 9, pp. 4671–4696.
  • 6C. Calgaro, E. Creusé, T. Goudon.

    Modeling and simulation of mixture flows: application to powder-snow avalanches, in: Comput. & Fluids, 2015, vol. 107, pp. 100–122.

    http://dx.doi.org/10.1016/j.compfluid.2014.10.008
  • 7C. Cancès, C. Guichard.

    Convergence of a nonlinear entropy diminishing Control Volume Finite Element scheme for solving anisotropic degenerate parabolic equations, in: Mathematics of Computation, 2016, vol. 85, no 298, pp. 549-580.

    https://hal.archives-ouvertes.fr/hal-00955091
  • 8C. Chainais-Hillairet.

    Entropy method and asymptotic behaviours of finite volume schemes, in: Finite volumes for complex applications. VII. Methods and theoretical aspects, Springer Proc. Math. Stat., Springer, Cham, 2014, vol. 77, pp. 17–35.
  • 9E. Creusé, S. Nicaise, G. Kunert.

    A posteriori error estimation for the Stokes problem: anisotropic and isotropic discretizations, in: Math. Models Methods Appl. Sci., 2004, vol. 14, no 9, pp. 1297–1341.

    http://dx.doi.org/10.1142/S0218202504003635
  • 10E. Creusé, S. Nicaise, Z. Tang, Y. Le Menach, N. Nemitz, F. Piriou.

    Residual-based a posteriori estimators for the 𝐀-φ magnetodynamic harmonic formulation of the Maxwell system, in: Math. Models Methods Appl. Sci., 2012, vol. 22, no 5, 1150028, 30 p.

    http://dx.doi.org/10.1142/S021820251150028X
Publications of the year

Articles in International Peer-Reviewed Journals

  • 11P. F. Antonietti, B. Merlet, M. Pierre, M. Verani.

    Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equation, in: AIMS Mathematics, August 2016, vol. 1, no 3, pp. 178-194.

    https://hal.archives-ouvertes.fr/hal-01355956
  • 12C. Besse, M. Ehrhardt, I. Lacroix-Violet.

    Discrete Artificial Boundary Conditions for the Korteweg-de Vries Equation, in: Numerical Methods for Partial Differential Equations, 2016, vol. 35, no 5, pp. 1455-1484.

    https://hal.archives-ouvertes.fr/hal-01105043
  • 13M. Bessemoulin-Chatard, C. Chainais-Hillairet.

    Exponential decay of a finite volume scheme to the thermal equilibrium for drift–diffusion systems, in: Journal of Numerical Mathematics, July 2016.

    https://hal.archives-ouvertes.fr/hal-01250709
  • 14C. Calgaro, M. Ezzoug, E. Zahrouni.

    On the global existence of weak solution for a multiphasic incompressible fluid model with Korteweg stress, in: Mathematical Methods in the Applied Sciences, 2016. [ DOI : 10.1002/mma.3969 ]

    https://hal.archives-ouvertes.fr/hal-01388718
  • 15C. Cancès, F. Coquel, E. Godlewski, H. Mathis, N. Seguin.

    Error analysis of a dynamic model adaptation procedure for nonlinear hyperbolic equations, in: Communications in Mathematical Sciences, 2016, vol. 14, no 1, pp. 1-30.

    https://hal.archives-ouvertes.fr/hal-00852101
  • 16C. Cancès, C. Guichard.

    Convergence of a nonlinear entropy diminishing Control Volume Finite Element scheme for solving anisotropic degenerate parabolic equations, in: Mathematics of Computation, 2016, vol. 85, no 298, pp. 549-580.

    https://hal.archives-ouvertes.fr/hal-00955091
  • 17C. Cancès, H. Mathis, N. Seguin.

    Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws, in: SIAM Journal on Numerical Analysis, 2016, vol. 54, no 2, pp. 1263-1287.

    https://hal.archives-ouvertes.fr/hal-00798287
  • 18C. Chainais-Hillairet, T. Gallouët.

    Study of a pseudo-stationary state for a corrosion model: existence and numerical approximation, in: Nonlinear Analysis: Real World Applications, 2016.

    https://hal.inria.fr/hal-01147621
  • 19C. Chainais-Hillairet, A. Jüngel, S. Schuchnigg.

    Entropy-dissipative discretization of nonlinear diffusion equations and discrete Beckner inequalities, in: Modelisation Mathématique et Analyse Numérique, 2016, vol. 50, no 1, pp. 135-162.

    https://hal.archives-ouvertes.fr/hal-00924282
  • 20C. Chen, E. Creusé, S. Nicaise, Z. Tang.

    Residual-based a posteriori estimators for the potential formulations of electrostatic and time-harmonic eddy current problems with voltage or current excitation, in: International Journal for Numerical Methods in Engineering, 2016, vol. 107, no 5, 18 p.

    https://hal.inria.fr/hal-01390241
  • 21P.-E. Jabin, T. Rey.

    Hydrodynamic limit of granular gases to pressureless Euler in dimension 1, in: Quarterly of Applied Mathematics, July 2016, 26 p, 23 pages, 1 figure. [ DOI : 10.1090/qam/1442. ]

    https://hal.archives-ouvertes.fr/hal-01279961
  • 22T. Rey, C. Tan.

    An Exact Rescaling Velocity Method for some Kinetic Flocking Models, in: SIAM Journal on Numerical Analysis, 2016, vol. 54, no 2, pp. 641–664, 21 pages, 6 figures. [ DOI : 10.1137/140993430. ]

    https://hal.archives-ouvertes.fr/hal-01078298
  • 23R. Tittarelli, Y. Le Menach, E. Creusé, S. Nicaise, F. Piriou, O. Moreau, O. Boiteau.

    Space-time residual-based a posteriori estimator for the A-phi formulation in eddy current problems, in: IEEE Transactions on Magnetics, 2016, vol. 51, no 3.

    https://hal.inria.fr/hal-01390250

Other Publications

References in notes
  • 37R. Abgrall.

    A review of residual distribution schemes for hyperbolic and parabolic problems: the July 2010 state of the art, in: Commun. Comput. Phys., 2012, vol. 11, no 4, pp. 1043–1080.

    http://dx.doi.org/10.4208/cicp.270710.130711s
  • 38R. Abgrall, G. Baurin, A. Krust, D. de Santis, M. Ricchiuto.

    Numerical approximation of parabolic problems by residual distribution schemes, in: Internat. J. Numer. Methods Fluids, 2013, vol. 71, no 9, pp. 1191–1206.

    http://dx.doi.org/10.1002/fld.3710
  • 39R. Abgrall, A. Larat, M. Ricchiuto.

    Construction of very high order residual distribution schemes for steady inviscid flow problems on hybrid unstructured meshes, in: J. Comput. Phys., 2011, vol. 230, no 11, pp. 4103–4136.

    http://dx.doi.org/10.1016/j.jcp.2010.07.035
  • 40R. Abgrall, A. Larat, M. Ricchiuto, C. Tavé.

    A simple construction of very high order non-oscillatory compact schemes on unstructured meshes, in: Comput. & Fluids, 2009, vol. 38, no 7, pp. 1314–1323.

    http://dx.doi.org/10.1016/j.compfluid.2008.01.031
  • 41T. Aiki, A. Muntean.

    A free-boundary problem for concrete carbonation: front nucleation and rigorous justification of the t-law of propagation, in: Interfaces Free Bound., 2013, vol. 15, no 2, pp. 167–180.

    http://dx.doi.org/10.4171/IFB/299
  • 42A. Alonso Rodríguez, A. Valli.

    Voltage and current excitation for time-harmonic eddy-current problems, in: SIAM J. Appl. Math., 2008, vol. 68, no 5, pp. 1477–1494.

    http://dx.doi.org/10.1137/070697677
  • 43B. Amaziane, A. Bergam, M. El Ossmani, Z. Mghazli.

    A posteriori estimators for vertex centred finite volume discretization of a convection-diffusion-reaction equation arising in flow in porous media, in: Internat. J. Numer. Methods Fluids, 2009, vol. 59, no 3, pp. 259–284.

    http://dx.doi.org/10.1002/fld.1456
  • 44I. Babuška, W. C. Rheinboldt.

    Error estimates for adaptive finite element computations, in: SIAM J. Numer. Anal., 1978, vol. 15, no 4, pp. 736–754.
  • 45J. Bear, Y. Bachmat.

    Introduction to modeling of transport phenomena in porous media, Springer, 1990, vol. 4.
  • 46J. Bear.

    Dynamic of Fluids in Porous Media, American Elsevier, New York, 1972.
  • 47S. Berrone, V. Garbero, M. Marro.

    Numerical simulation of low-Reynolds number flows past rectangular cylinders based on adaptive finite element and finite volume methods, in: Comput. & Fluids, 2011, vol. 40, pp. 92–112.

    http://dx.doi.org/10.1016/j.compfluid.2010.08.014
  • 48D. Bresch, E. H. Essoufi, M. Sy.

    Effect of density dependent viscosities on multiphasic incompressible fluid models, in: J. Math. Fluid Mech., 2007, vol. 9, no 3, pp. 377–397.
  • 49C. Cancès, T. O. Gallouët, L. Monsaingeon.

    The gradient flow structure for incompressible immiscible two-phase flows in porous media, in: C. R. Math. Acad. Sci. Paris, 2015, vol. 353, no 11, pp. 985–989.

    http://dx.doi.org/10.1016/j.crma.2015.09.021
  • 50C. Cancès, I. S. Pop, M. Vohralík.

    An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow, in: Math. Comp., 2014, vol. 83, no 285, pp. 153–188.

    http://dx.doi.org/10.1090/S0025-5718-2013-02723-8
  • 51J. A. Carrillo, A. Jüngel, P. A. Markowich, G. Toscani, A. Unterreiter.

    Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, in: Monatsh. Math., 2001, vol. 133, no 1, pp. 1–82.

    http://dx.doi.org/10.1007/s006050170032
  • 52E. Creusé, S. Nicaise, Z. Tang, Y. Le Menach, N. Nemitz, F. Piriou.

    Residual-based a posteriori estimators for the 𝐓/Ω magnetodynamic harmonic formulation of the Maxwell system, in: Int. J. Numer. Anal. Model., 2013, vol. 10, no 2, pp. 411–429.
  • 53E. Creusé, S. Nicaise, E. Verhille.

    Robust equilibrated a posteriori error estimators for the Reissner-Mindlin system, in: Calcolo, 2011, vol. 48, no 4, pp. 307–335.

    http://dx.doi.org/10.1007/s10092-011-0042-0
  • 54D. A. Di Pietro, M. Vohralík.

    A Review of Recent Advances in Discretization Methods, a Posteriori Error Analysis, and Adaptive Algorithms for Numerical Modeling in Geosciences, in: Oil & Gas Science and Technology-Rev. IFP, June 2014, pp. 1-29, (online first).
  • 55G. Dimarco, R. Loubere.

    Towards an ultra efficient kinetic scheme. Part I: Basics on the BGK equation, in: J. Comput. Phys., 2013, vol. 255, pp. 680–698.

    http://dx.doi.org/10.1016/j.jcp.2012.10.058
  • 56G. Dimarco, R. Loubere.

    Towards an ultra efficient kinetic scheme. Part II: The high order case, in: J. Comput. Phys., 2013, vol. 255, pp. 699–719.

    http://dx.doi.org/10.1016/j.jcp.2013.07.017
  • 57V. Dolejší, A. Ern, M. Vohralík.

    A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems, in: SIAM J. Numer. Anal., 2013, vol. 51, no 2, pp. 773–793.

    http://dx.doi.org/10.1137/110859282
  • 58J. Droniou.

    Finite volume schemes for diffusion equations: introduction to and review of modern methods, in: Math. Models Methods Appl. Sci., 2014, vol. 24, no 8, pp. 1575-1620.
  • 59E. Emmrich.

    Two-step BDF time discretisation of nonlinear evolution problems governed by monotone operators with strongly continuous perturbations, in: Comput. Methods Appl. Math., 2009, vol. 9, no 1, pp. 37–62.
  • 60L. Gosse.

    Computing qualitatively correct approximations of balance laws, SIMAI Springer Series, Springer, Milan, 2013, vol. 2, xx+340 p, Exponential-fit, well-balanced and asymptotic-preserving.

    http://dx.doi.org/10.1007/978-88-470-2892-0
  • 61L. Greengard, J.-Y. Lee.

    Accelerating the nonuniform fast Fourier transform, in: SIAM Rev., 2004, vol. 46, no 3, pp. 443–454.

    http://dx.doi.org/10.1137/S003614450343200X
  • 62F. Guillén-González, J. V. Gutiérrez-Santacreu.

    Conditional stability and convergence of a fully discrete scheme for three-dimensional Navier-Stokes equations with mass diffusion, in: SIAM J. Numer. Anal., 2008, vol. 46, no 5, pp. 2276–2308.

    http://dx.doi.org/10.1137/07067951X
  • 63R. Hiptmair, O. Sterz.

    Current and voltage excitations for the eddy current model, in: International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2005, vol. 18, no 1, pp. 1–21.
  • 64M. E. Hubbard, M. Ricchiuto.

    Discontinuous upwind residual distribution: a route to unconditional positivity and high order accuracy, in: Comput. & Fluids, 2011, vol. 46, pp. 263–269.

    http://dx.doi.org/10.1016/j.compfluid.2010.12.023
  • 65S. Jin.

    Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations, in: SIAM, J. Sci. Comput., 1999, vol. 21, pp. 441-454.
  • 66R. Jordan, D. Kinderlehrer, F. Otto.

    The variational formulation of the Fokker-Planck equation, in: SIAM J. Math. Anal., 1998, vol. 29, no 1, pp. 1–17.
  • 67D. D. Joseph.

    Fluid dynamics of two miscible liquids with diffusion and gradient stresses, in: European J. Mech. B Fluids, 1990, vol. 9, no 6, pp. 565–596.
  • 68A. V. Kazhikhov, S. Smagulov.

    The correctness of boundary value problems in a diffusion model in an inhomogeneous fluid, in: Sov. Phys. Dokl., 1977, vol. 22, pp. 249–250.
  • 69C. Liu, N. J. Walkington.

    Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity, in: SIAM J. Numer. Anal., 2007, vol. 45, no 3, pp. 1287–1304 (electronic).

    http://dx.doi.org/10.1137/050629008
  • 70P. Mason, A. Aftalion.

    Classification of the ground states and topological defects in a rotating two-component Bose-Einstein condensate, in: Phys. Rev. A, 2011, vol. 84, no 3, 033611.
  • 71A. Mellet, A. Vasseur.

    On the barotropic compressible Navier-Stokes equations, in: Comm. Partial Differential Equations, 2007, vol. 32, no 1-3, pp. 431–452.

    http://dx.doi.org/10.1080/03605300600857079
  • 72F. Otto.

    The geometry of dissipative evolution equations: the porous medium equation, in: Comm. Partial Differential Equations, 2001, vol. 26, no 1-2, pp. 101–174.
  • 73M. Ricchiuto, R. Abgrall.

    Explicit Runge-Kutta residual distribution schemes for time dependent problems: second order case, in: J. Comput. Phys., 2010, vol. 229, no 16, pp. 5653–5691.

    http://dx.doi.org/10.1016/j.jcp.2010.04.002
  • 74F. Santambrogio.

    Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling, Progress in Nonlinear Differential Equations and Their Applications 87, 1, Birkhäuser Basel, 2015.

    http://gen.lib.rus.ec/book/index.php?md5=24B4AA557102EC12148F101DF2C91937
  • 75C. Villani.

    Optimal transport, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 2009, vol. 338, xxii+973 p, Old and new.

    http://dx.doi.org/10.1007/978-3-540-71050-9
  • 76M. Vohralík.

    Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods, in: Numer. Math., 2008, vol. 111, no 1, pp. 121–158.

    http://dx.doi.org/10.1007/s00211-008-0168-4
  • 77J. de Frutos, B. García-Archilla, J. Novo.

    A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations, in: J. Comput. Appl. Math., 2011, vol. 236, no 6, pp. 1103–1122.

    http://dx.doi.org/10.1016/j.cam.2011.07.033


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