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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, Y. Penel.

    Positivity-preserving schemes for Euler equations: Sharp and practical CFL conditions, in: J. Comput. Phys., 2013, vol. 234, no 1, pp. 417–438.
  • 7C. 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.
  • 8E. 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
  • 9E. 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

Doctoral Dissertations and Habilitation Theses

  • 10C. Cancès.

    Analyse mathématique et numérique d'équations aux dérivées partielles issues de la mécanique des fluides : applications aux écoulements en milieux poreux, Université Pierre et Marie Curie , December 2015, Habilitation à diriger des recherches.

    https://hal.archives-ouvertes.fr/tel-01239700

Articles in International Peer-Reviewed Journals

  • 11B. Andreianov, C. Cancès.

    On interface transmission conditions for conservation laws with discontinuous flux of general shape, in: Journal of Hyperbolic Differential Equations, July 2015, vol. 12, no 2, pp. 343-384. [ DOI : 10.1142/S0219891615500101 ]

    https://hal.archives-ouvertes.fr/hal-00940756
  • 12C. Calgaro, C. Emmanuel, G. Thierry.

    Modeling and simulation of mixture flows: Application to powder–snow avalanches, in: Computers and Fluids, January 2015, vol. 107, pp. 100-122. [ DOI : 10.1016/j.compfluid.2014.10.008 ]

    https://hal.archives-ouvertes.fr/hal-01248897
  • 13C. 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
  • 14C. Cancès, T. Gallouët, L. Monsaingeon.

    The gradient flow structure for incompressible immiscible two-phase flows in porous media, in: Comptes rendus de l'académie des sciences, Mathématiques, 2015, vol. 353, pp. 985-989.

    https://hal.archives-ouvertes.fr/hal-01122770
  • 15C. 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
  • 16C. Chainais-Hillairet, P.-L. Colin, I. Lacroix-Violet.

    Convergence of a Finite Volume Scheme for a Corrosion Model, in: International Journal on Finite Volumes, 2015. [ DOI : 10.1007/978-3-319-05591-6_54 ]

    https://hal.archives-ouvertes.fr/hal-01082041
  • 17C. 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
  • 18C. Chainais-Hillairet, A. Jüngel, P. Shpartko.

    A finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors, in: Numerical Methods for Partial Differential Equations, November 2015. [ DOI : 10.1002/num.22030 ]

    https://hal.archives-ouvertes.fr/hal-01115858
  • 19C. Chainais-Hillairet, I. Lacroix-Violet.

    On the existence of solutions for a drift-diffusion system arising in corrosion modelling, in: Discrete and Continuous Dynamical Systems - Series B, 2015, vol. 20, no Issue 1, 15 p.

    https://hal.archives-ouvertes.fr/hal-00764239
  • 20E. Creusé, M. Farhloul, S. Nicaise, L. Paquet.

    A posteriori error estimates of the stabilized Crouzeix-Raviart finite element method for the Lamé-Navier equations, in: Far East Journal of Mathematical Sciences, 2015, vol. 96, no 2, pp. 167-192.

    https://hal.archives-ouvertes.fr/hal-00777678
  • 21P. Dular, Y. Le Menach, Z. Tang, E. Creusé, F. Piriou.

    Finite element mesh adaptation strategies from residual and hierarchical error estimators in eddy current problems, in: IEEE Transactions on Magnetics, 2015, vol. 51, no 3. [ DOI : 10.1109/TMAG.2014.2352553 ]

    https://hal.archives-ouvertes.fr/hal-01243654
  • 22F. Filbet, L. Pareschi, T. Rey.

    On steady-state preserving spectral methods for homogeneous Boltzmann equations, in: Comptes Rendus Mathématique, April 2015, vol. 353, no 4, pp. 309–314. [ DOI : 10.1016/j.crma.2015.01.015. ]

    https://hal.inria.fr/hal-01053930
  • 23F. Filbet, T. Rey.

    A hierarchy of hybrid numerical methods for multi-scale kinetic equations, in: SIAM Journal on Scientific Computing, May 2015, vol. 37, no 3, pp. A1218–A1247.

    https://hal.archives-ouvertes.fr/hal-00951980
  • 24M. I. Garcia De Soria, P. Maynar, S. Mischler, C. Mouhot, T. Rey, E. Trizac.

    Towards an H-theorem for granular gases, in: Journal of Statistical Mechanics: Theory and Experiment, December 2015, vol. 2015, 14 pages, 5 figures. [ DOI : 10.1088/1742-5468/2015/11/P11009 ]

    https://hal.archives-ouvertes.fr/hal-01242931
  • 25M. Gisclon, I. Lacroix-Violet.

    About the barotropic compressible quantum Navier-Stokes equations, in: Nonlinear Analysis: Theory, Methods and Applications, 2015, vol. 128.

    https://hal.archives-ouvertes.fr/hal-01090191
  • 26D. H. MAC, Z. Tang, S. CLENET, E. Creusé.

    Residual-based a posteriori error estimation for a stochastic magnetostatic problem, in: Journal of Computational and Applied Mathematics, 2015, vol. 289, pp. 51-67. [ DOI : 10.1016/j.cam.2015.03.027 ]

    https://hal.archives-ouvertes.fr/hal-01243687
  • 27H. Mathis, C. Cancès, E. Godlewski, N. Seguin.

    Dynamic model adaptation for multiscale simulation of hyperbolic systems with relaxation, in: Journal of Scientific Computing, 2015, vol. 63, no 3, pp. 820-861.

    https://hal.archives-ouvertes.fr/hal-00782637
  • 28Z. Tang, Y. Le Menach, E. Creusé, S. Nicaise, F. Piriou, N. Nemitz.

    A posteriori residual error estimators with mixed boundary conditions for quasi-static electromagnetic problems, in: COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2015, vol. 34, no 3, pp. 724-739. [ DOI : 10.1108/COMPEL-10-2014-0256 ]

    https://hal.archives-ouvertes.fr/hal-01243637
  • 29Z. Tang, Y. Le Menach, E. Creusé, S. Nicaise, F. Piriou.

    Residual a posteriori estimator for magnetoharmonic potential formulations with global quantities source terms, in: IEEE Transactions on Magnetics, 2015, vol. 51, no 3. [ DOI : 10.1109/TMAG.2014.2359770 ]

    https://hal.archives-ouvertes.fr/hal-01243666

Other Publications

References in notes
  • 40R. 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
  • 41R. 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
  • 42R. 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
  • 43R. 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
  • 44B. 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
  • 45I. Babuška, W. C. Rheinboldt.

    Error estimates for adaptive finite element computations, in: SIAM J. Numer. Anal., 1978, vol. 15, no 4, pp. 736–754.
  • 46J. Bear, Y. Bachmat.

    Introduction to modeling of transport phenomena in porous media, Springer, 1990, vol. 4.
  • 47J. Bear.

    Dynamic of Fluids in Porous Media, American Elsevier, New York, 1972.
  • 48S. 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
  • 49C. 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
  • 50J. 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
  • 51E. 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.
  • 52E. 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
  • 53D. 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).
  • 54V. 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
  • 55J. 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.
  • 56E. 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.
  • 57R. Eymard, C. Guichard, R. Herbin.

    Small-stencil 3D schemes for diffusive flows in porous media, in: ESAIM Math. Model. Numer. Anal., 2012, vol. 46, no 2, pp. 265–290.

    http://dx.doi.org/10.1051/m2an/2011040
  • 58F. 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
  • 59M. 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
  • 60S. Jin.

    Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations, in: SIAM, J. Sci. Comput., 1999, vol. 21, pp. 441-454.
  • 61A. 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.
  • 62C. 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
  • 63P. 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 p.
  • 64A. Mielke.

    A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems, in: Nonlinearity, 2011, vol. 24, no 4, pp. 1329–1346.

    http://dx.doi.org/10.1088/0951-7715/24/4/016
  • 65F. 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.
  • 66M. 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
  • 67M. 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
  • 68J. 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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