Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Dissemination
Bibliography
XML PDF e-pub
PDF e-Pub


Bibliography

Major publications by the team in recent years
[1]
M. 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, 2017, vol. 25, no 3, pp. 147-168. [ DOI : 10.1515/jnma-2016-0007 ]
https://hal.archives-ouvertes.fr/hal-01250709
[2]
C. Calgaro, E. Creusé, T. Goudon, S. Krell.
Simulations of non homogeneous viscous flows with incompressibility constraints, in: Mathematics and Computers in Simulation, 2017, vol. 137, pp. 201-225.
https://hal.archives-ouvertes.fr/hal-01246070
[3]
C. Cancès, T. Gallouët, L. Monsaingeon.
Incompressible immiscible multiphase flows in porous media: a variational approach, in: Analysis & PDE, 2017, vol. 10, no 8, pp. 1845–1876. [ DOI : 10.2140/apde.2017.10.1845 ]
https://hal.archives-ouvertes.fr/hal-01345438
[4]
C. Cancès, C. Guichard.
Numerical analysis of a robust free energy diminishing Finite Volume scheme for parabolic equations with gradient structure, in: Foundations of Computational Mathematics, 2017, vol. 17, no 6, pp. 1525-1584.
https://hal.archives-ouvertes.fr/hal-01119735
[5]
C. Chainais-Hillairet, B. Merlet, A. Vasseur.
Positive Lower Bound for the Numerical Solution of a Convection-Diffusion Equation, in: FVCA8 2017 - International Conference on Finite Volumes for Complex Applications VIII, Lille, France, Springer, June 2017, pp. 331-339. [ DOI : 10.1007/978-3-319-57397-7_26 ]
https://hal.archives-ouvertes.fr/hal-01596076
[6]
D. A. Di Pietro, A. Ern, S. Lemaire.
An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators, in: Computational Methods in Applied Mathematics, June 2014, vol. 14, no 4, pp. 461-472. [ DOI : 10.1515/cmam-2014-0018 ]
https://hal.archives-ouvertes.fr/hal-00978198
[7]
G. Dimarco, R. Loubère, J. Narski, T. Rey.
An efficient numerical method for solving the Boltzmann equation in multidimensions, in: Journal of Computational Physics, 2018, vol. 353, pp. 46-81. [ DOI : 10.1016/j.jcp.2017.10.010 ]
https://hal.archives-ouvertes.fr/hal-01357112
[8]
F. Filbet, M. Herda.
A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure, in: Numerische Mathematik, 2017, vol. 137, no 3, pp. 535-577.
https://hal.archives-ouvertes.fr/hal-01326029
[9]
I. Lacroix-Violet, A. Vasseur.
Global weak solutions to the compressible quantum Navier–Stokes equation and its semi-classical limit, in: Journal de Mathématiques Pures et Appliquées, 2018, vol. 114, pp. 191-210.
https://hal.archives-ouvertes.fr/hal-01347943
[10]
B. Merlet.
A highly anisotropic nonlinear elasticity model for vesicles I. Eulerian formulation, rigidity estimates and vanishing energy limit, in: Arch. Ration. Mech. Anal., 2015, vol. 217, no 2, pp. 651–680. [ DOI : 10.1007/s00205-014-0839-5 ]
https://hal.archives-ouvertes.fr/hal-00848547
Publications of the year

Doctoral Dissertations and Habilitation Theses

[11]
A. Zurek.
Free boundary problems for the degradation of materials and biofilms growth: numerical analysis and modelisation, Université de Lille, September 2019.
https://tel.archives-ouvertes.fr/tel-02397231
[12]
c. colin.
Analysis and numerical simulation by a combined Finite Volumes - Finite Elements method of low Mach type models, Université de Lille / Laboratoire Paul Painlevé, May 2019.
https://hal.archives-ouvertes.fr/tel-02406716

Articles in International Peer-Reviewed Journals

[13]
A. Ait Hammou Oulhaj, C. Cancès, C. Chainais-Hillairet, P. Laurençot.
Large time behavior of a two phase extension of the porous medium equation, in: Interfaces and Free Boundaries, 2019, vol. 21, pp. 199-229, https://arxiv.org/abs/1803.10476. [ DOI : 10.4171/IFB/421 ]
https://hal.archives-ouvertes.fr/hal-01752759
[14]
A. Ait Hammou Oulhaj, D. Maltese.
Convergence of a positive nonlinear control volume finite element scheme for an anisotropic seawater intrusion model with sharp interfaces, in: Numerical Methods for Partial Differential Equations, 2020, vol. 36, no 1, pp. 133-153. [ DOI : 10.1002/num.22422 ]
https://hal.archives-ouvertes.fr/hal-01906872
[15]
C. Besse, S. Descombes, G. Dujardin, I. Lacroix-Violet.
Energy preserving methods for nonlinear Schrödinger equations, in: IMA Journal of Numerical Analysis, 2019, forthcoming. [ DOI : 10.1016/j.apnum.2019.11.008 ]
https://hal.archives-ouvertes.fr/hal-01951527
[16]
M. Bessemoulin-Chatard, C. Chainais-Hillairet.
Uniform-in-time Bounds for approximate Solutions of the drift-diffusion System, in: Numerische Mathematik, 2019, vol. 141, no 4, pp. 881-916. [ DOI : 10.1007/s00211-018-01019-1 ]
https://hal.archives-ouvertes.fr/hal-01659418
[17]
M. Bessemoulin-Chatard, M. Herda, T. Rey.
Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations, in: Mathematics of Computation, September 2019, 39 pages. [ DOI : 10.1090/mcom/3490 ]
https://hal.archives-ouvertes.fr/hal-01957832
[18]
O. Blondel, C. Cancès, M. Sasada, M. Simon.
Convergence of a Degenerate Microscopic Dynamics to the Porous Medium Equation, in: Annales de l'Institut Fourier, 2019, forthcoming.
https://hal.archives-ouvertes.fr/hal-01710628
[19]
D. Bresch, M. Gisclon, I. Lacroix-Violet.
On Navier-Stokes-Korteweg and Euler-Korteweg Systems: Application to Quantum Fluids Models, in: Archive for Rational Mechanics and Analysis, 2019, vol. 233, no 3, pp. 975-1025, https://arxiv.org/abs/1703.09460. [ DOI : 10.1007/s00205-019-01373-w ]
https://hal.archives-ouvertes.fr/hal-01496960
[20]
C. Calgaro, C. Colin, E. Creusé.
A combined finite volume - finite element scheme for a low-Mach system involving a Joule term, in: AIMS Mathematics, 2019, vol. 5, no 1, pp. 311-331, forthcoming.
https://hal.archives-ouvertes.fr/hal-02398893
[21]
C. Calgaro, c. colin, E. Creusé.
A combined Finite Volumes -Finite Elements method for a low-Mach model, in: International Journal for Numerical Methods in Fluids, 2019, vol. 90, no 1, pp. 1-21. [ DOI : 10.1002/fld.4706 ]
https://hal.archives-ouvertes.fr/hal-01574894
[22]
C. Calgaro, c. colin, E. Creusé, E. Zahrouni.
Approximation by an iterative method of a low Mach model with temperature dependent viscosity, in: Mathematical Methods in the Applied Sciences, 2019, vol. 42, no 1, pp. 250-271. [ DOI : 10.1002/mma.5342 ]
https://hal.archives-ouvertes.fr/hal-01801242
[23]
C. Cancès, C. Chainais-Hillairet, A. Gerstenmayer, A. Jüngel.
Convergence of a Finite-Volume Scheme for a Degenerate Cross-Diffusion Model for Ion Transport, in: Numerical Methods for Partial Differential Equations, 2019, vol. 35, no 2, pp. 545-575, https://arxiv.org/abs/1801.09408. [ DOI : 10.1002/num.22313 ]
https://hal.archives-ouvertes.fr/hal-01695129
[24]
C. Cancès, T. Gallouët, M. Laborde, L. Monsaingeon.
Simulation of multiphase porous media flows with minimizing movement and finite volume schemes, in: European Journal of Applied Mathematics, 2019, vol. 30, no 6, pp. 1123-1152. [ DOI : 10.1017/S0956792518000633 ]
https://hal.archives-ouvertes.fr/hal-01700952
[25]
C. Cancès, D. Matthes, F. Nabet.
A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow, in: Archive for Rational Mechanics and Analysis, 2019, vol. 233, no 2, pp. 837–866. [ DOI : 10.1007/s00205-019-01369-6 ]
https://hal.archives-ouvertes.fr/hal-01665338
[26]
C. Chainais-Hillairet, M. Herda.
Large-time behaviour of a family of finite volume schemes for boundary-driven convection-diffusion equations, in: IMA Journal of Numerical Analysis, November 2019, https://arxiv.org/abs/1810.01087, forthcoming. [ DOI : 10.1093/imanum/drz037 ]
https://hal.archives-ouvertes.fr/hal-01885015
[27]
A. Chambolle, L. A. D. Ferrari, B. Merlet.
A phase-field approximation of the Steiner problem in dimension two, in: Advances in Calculus of Variation, 2019, vol. 12, no 2, pp. 157–179, https://arxiv.org/abs/1609.00519v1 - 27 pages, 8 figures. [ DOI : 10.1515/acv-2016-0034 ]
https://hal.archives-ouvertes.fr/hal-01359483
[28]
A. Chambolle, L. A. D. Ferrari, B. Merlet.
Strong approximation in h-mass of rectifiable currents under homological constraint, in: Advances in Calculus of Variation, 2019, https://arxiv.org/abs/1806.05046, forthcoming. [ DOI : 10.1515/acv-2018-0079 ]
https://hal.archives-ouvertes.fr/hal-01813234
[29]
A. Chambolle, L. A. D. Ferrari, B. Merlet.
Variational approximation of size-mass energies for k-dimensional currents, in: ESAIM: Control, Optimisation and Calculus of Variations, 2019, vol. 25 (2019), no 43, 39 p, https://arxiv.org/abs/1710.08808, forthcoming.
https://hal.archives-ouvertes.fr/hal-01622540
[30]
M. Cicuttin, A. Ern, S. Lemaire.
A Hybrid High-Order method for highly oscillatory elliptic problems, in: Computational Methods in Applied Mathematics, 2019, vol. 19, no 4, pp. 723-748. [ DOI : 10.1515/cmam-2018-0013 ]
https://hal.archives-ouvertes.fr/hal-01467434
[31]
E. Creusé, P. Dular, S. Nicaise.
About the gauge conditions arising in Finite Element magnetostatic problems, in: Computers and Mathematics with Applications, 2019, vol. 77, no 6, pp. 1563-1582.
https://hal.archives-ouvertes.fr/hal-01955649
[32]
E. Creusé, Y. Le Menach, S. Nicaise, F. Piriou, R. Tittarelli.
Two Guaranteed Equilibrated Error Estimators for Harmonic Formulations in Eddy Current Problems, in: Computers and Mathematics with Applications, 2019, vol. 77, no 6, pp. 1549-1562.
https://hal.archives-ouvertes.fr/hal-01955692
[33]
M. Goldman, B. Merlet.
Recent results on non-convex functionals penalizing oblique oscillations, in: Rendiconti del Seminario Matematico, 2019.
https://hal.archives-ouvertes.fr/hal-02382214
[34]
M. Goldman, B. Merlet, V. Millot.
A Ginzburg-Landau model with topologically induced free discontinuities, in: Annales de l'Institut Fourier, 2019, forthcoming.
https://hal.archives-ouvertes.fr/hal-01643795
[35]
M. Herda, L. M. Rodrigues.
Anisotropic Boltzmann-Gibbs dynamics of strongly magnetized Vlasov-Fokker-Planck equations, in: Kinetic and Related Models , 2019, vol. 12, no 3, pp. 593-636, https://arxiv.org/abs/1610.05138. [ DOI : 10.3934/krm.2019024 ]
https://hal.archives-ouvertes.fr/hal-01382854
[36]
S. Lemaire.
Bridging the Hybrid High-Order and Virtual Element methods, in: IMA Journal of Numerical Analysis, 2019, forthcoming.
https://hal.archives-ouvertes.fr/hal-01902962
[37]
W. Melis, T. Rey, G. Samaey.
Projective and telescopic projective integration for the nonlinear BGK and Boltzmann equations, in: SMAI Journal of Computational Mathematics, 2019, vol. 5, pp. 53-88, https://arxiv.org/abs/1712.06362. [ DOI : 10.5802/smai-jcm.43 ]
https://hal.archives-ouvertes.fr/hal-01666346
[38]
N. Peton, C. Cancès, D. Granjeon, Q.-H. Tran, S. Wolf.
Numerical scheme for a water flow-driven forward stratigraphic model, in: Computational Geosciences, 2019, forthcoming. [ DOI : 10.1007/s10596-019-09893-w ]
https://hal.archives-ouvertes.fr/hal-01870347
[39]
A. Zurek.
Numerical approximation of a concrete carbonation model: study of the t-law of propagation, in: Numerical Methods for Partial Differential Equations, May 2019, vol. 35, no 5, pp. 1801-1820. [ DOI : 10.1002/num.22377 ]
https://hal.archives-ouvertes.fr/hal-01839277

International Conferences with Proceedings

[40]
M. Cicuttin, A. Ern, S. Lemaire.
On the implementation of a multiscale Hybrid High-Order method, in: ENUMATH 2017, Bergen, Norway, I. Berre, K. Kumar, J. M. Nordbotten, I. S. Pop, F. A. Radu (editors), Numerical Mathematics and Advanced Applications - ENUMATH 2017, Springer, Cham, 2019, vol. 126, pp. 509-517. [ DOI : 10.1007/978-3-319-96415-7_46 ]
https://hal.archives-ouvertes.fr/hal-01661925
[41]
D. Matthes, C. Cancès, F. Nabet.
A degenerate Cahn‐Hilliard model as constrained Wasserstein gradient flow, in: GAMM annual meeting, Vienna, Austria, International Association for Applied Mathematics and Mechanics, November 2019, vol. 19, no 1. [ DOI : 10.1002/pamm.201900158 ]
https://hal.archives-ouvertes.fr/hal-02377146

Software

[42]
A. Mouton, C. Calgaro, E. Creusé.
NS2DDV - Navier-Stokes 2D à Densité Variable, September 2019,
[ SWH-ID : swh:1:dir:a126af9f1534e0b9f3431531a5f4751ad9b7b2fe ]
, Software.
https://hal.archives-ouvertes.fr/hal-02137040

Other Publications

[43]
F. Alouges, A. de Bouard, B. Merlet, L. Nicolas.
Stochastic homogenization of the Landau-Lifshitz-Gilbert equation, February 2019, https://arxiv.org/abs/1902.05743 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02020241
[44]
N. Ayi, M. Herda, H. Hivert, I. Tristani.
A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium, December 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02389146
[45]
S. Billiard, M. Derex, L. Maisonneuve, T. Rey.
Convergence of knowledge in a cultural evolution model with population structure, random social learning and credibility biases, November 2019, 25 pages.
https://hal.archives-ouvertes.fr/hal-02357188
[46]
C. Calgaro, E. Creusé.
A finite volume method for a convection- diffusion equation involving a Joule term, 2019, working paper or preprint.
https://hal.inria.fr/hal-02432936
[47]
M. Campos Pinto, F. Charles, B. Després, M. Herda.
A projection algorithm on the set of polynomials with two bounds, May 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02128851
[48]
C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, B. Gaudeul.
A numerical analysis focused comparison of several Finite Volume schemes for an Unipolar Degenerated Drift-Diffusion Model, December 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02194604
[49]
C. Cancès, C. Chainais-Hillairet, M. Herda, S. Krell.
Large time behavior of nonlinear finite volume schemes for convection-diffusion equations, November 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02360155
[50]
C. Cancès, T. O. Gallouët, G. Todeschi.
A variational finite volume scheme for Wasserstein gradient flows, July 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02189050
[51]
C. Cancès, B. Gaudeul.
Entropy diminishing finite volume approximation of a cross-diffusion system, 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02418908
[52]
C. Cancès, D. Maltese.
A gravity current model with capillary trapping for oil migration in multilayer geological basins, August 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02272965
[53]
C. Cancès, F. Nabet.
Energy stable discretization for two-phase porous media flows, January 2020, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02442233
[54]
C. Cancès, F. Nabet, M. Vohralík.
Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations, January 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01894884
[55]
C. Chainais-Hillairet, M. Herda.
L bounds for numerical solutions of noncoercive convection-diffusion equations, December 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02404546
[56]
C. Chainais-Hillairet, S. Krell.
Exponential decay to equilibrium of nonlinear DDFV schemes for convection-diffusion equations, December 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02408212
[57]
F. Chave.
Numerical study of the fracture diffusion-dispersion coefficient for passive transport in fractured porous media, December 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02412691
[58]
F. Chave, D. A. Di Pietro, S. Lemaire.
A three-dimensional Hybrid High-Order method for magnetostatics, December 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02407175
[59]
B. Després, M. Herda.
Computation of sum of squares polynomials from data points, August 2019, https://arxiv.org/abs/1812.02444 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01946539
[60]
G. Dujardin, I. Lacroix-Violet.
High order linearly implicit methods for evolution equations: How to solve an ODE by inverting only linear systems, November 2019, https://arxiv.org/abs/1911.06016 - working paper or preprint.
https://hal.inria.fr/hal-02361814
[61]
A. El Keurti, T. Rey.
Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions, December 2019, https://arxiv.org/abs/1912.06423 - 8 pages.
https://hal.archives-ouvertes.fr/hal-02408246
[62]
M. Goldman, B. Merlet.
Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimates, May 2019, https://arxiv.org/abs/1905.07905 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02132896
References in notes
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R. Abgrall.
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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.
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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.
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A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations, in: J. Comput. Phys., 2011, vol. 230, no 22, pp. 7988–8009.
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C. 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.
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L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini, A. Russo.
Basic principles of virtual element methods, in: Math. Models Methods Appl. Sci. (M3AS), 2013, vol. 23, no 1, pp. 199–214.
[76]
J.-D. Benamou, G. Carlier, M. Laborde.
An augmented Lagrangian approach to Wasserstein gradient flows and applications, in: Gradient flows: from theory to application, ESAIM Proc. Surveys, EDP Sci., Les Ulis, 2016, vol. 54, pp. 1–17.
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S. 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.
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[78]
C. Besse.
Analyse numérique des systèmes de Davey–Stewartson, Université Bordeaux 1, 1998.
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M. 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.
https://epubs.siam.org/doi/abs/10.1137/130913432
[80]
D. Bresch, P. Noble, J.-P. Vila.
Relative entropy for compressible Navier-Stokes equations with density dependent viscosities and various applications, in: LMLFN 2015—low velocity flows—application to low Mach and low Froude regimes, ESAIM Proc. Surveys, EDP Sci., Les Ulis, 2017, vol. 58, pp. 40–57.
[81]
C. 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.
[82]
C. 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
[83]
C. 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
[84]
C. 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
[85]
J. 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
[86]
C. 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.
[87]
C. 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.
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