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, n^o 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, n^o 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, n^o 4.
  http://epubs.siam.org/toc/sjnaam/52/4
• 4C. Calgaro, E. Chane-Kane, E. Creusé, T. Goudon.
  $L^{\infty }$-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, n^o 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, n^o 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, n^o 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, n^o 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 $𝐀-\phi$ magnetodynamic harmonic formulation of the Maxwell system, in: Math. Models Methods Appl. Sci., 2012, vol. 22, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 3.
  https://hal.inria.fr/hal-01390250

Other Publications

• 24A. Ait Hammou Oulhaj.
  Numerical analysis of a finite volume scheme for a seawater intrusion model with cross-diffusion in an unconfined aquifer, 2017, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01432197
• 25A. Ait Hammou Oulhaj, C. Cancès, C. Chainais-Hillairet.
  Numerical analysis of a nonlinearly stable and positive Control Volume Finite Element scheme for Richards equation with anisotropy, 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01372954
• 26K. Brenner, C. Cancès.
  Improving Newton's method performance by parametrization: the case of Richards equation, 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01342386
• 27C. Calgaro, E. Creusé, T. Goudon, S. Krell.
  Simulations of non homogeneous viscous flows with incompressibility constraints, 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01246070
• 28C. Calgaro, O. Goubet, E. Zahrouni.
  Finite dimensional global attractor for a semi-discrete fractional nonlinear Schrödinger equation, July 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01388788
• 29C. Cancès, T. Gallouët, L. Monsaingeon.
  Incompressible immiscible multiphase flows in porous media: a variational approach, 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01345438
• 30C. Cancès, C. Guichard.
  Numerical analysis of a robust free energy diminishing Finite Volume scheme for parabolic equations with gradient structure, 2016, to appear in Foundations of Computational Mathematics.
  https://hal.archives-ouvertes.fr/hal-01119735
• 31G. Dimarco, R. Loubère, J. Narski, T. Rey.
  An efficient numerical method for solving the Boltzmann equation in multidimensions, August 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01357112
• 32L. A. D. Ferrari, A. Chambolle, B. Merlet.
  A simple phase-field approximation of the Steiner problem in dimension two, September 2016, 24 pages, 8 figures.
  https://hal.archives-ouvertes.fr/hal-01359483
• 33M. Goldman, B. Merlet.
  Phase segregation for binary mixtures of Bose-Einstein Condensates, November 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01155676
• 34I. Lacroix-Violet, A. Vasseur.
  Global weak solutions to the compressible quantum navier-stokes equation and its semi-classical limit, July 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01347943
• 35F. Nabet.
  An error estimate for a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions, February 2016, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01273945
• 36L. Pareschi, T. Rey.
  Residual equilibrium schemes for time dependent partial differential equations, February 2016, 23 pages, 12 figures.
  https://hal.archives-ouvertes.fr/hal-01270297

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, n^o 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, n^o 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, n^o 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, n^o 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 $\sqrt{t}$-law of propagation, in: Interfaces Free Bound., 2013, vol. 15, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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 $𝐓/\Omega$ magnetodynamic harmonic formulation of the Maxwell system, in: Int. J. Numer. Anal. Model., 2013, vol. 10, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 3, 033611.
• 71A. Mellet, A. Vasseur.
  On the barotropic compressible Navier-Stokes equations, in: Comm. Partial Differential Equations, 2007, vol. 32, n^o 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, n^o 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, n^o 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, n^o 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, n^o 6, pp. 1103–1122.
  http://dx.doi.org/10.1016/j.cam.2011.07.033