Personnel
Overall Objectives
Research Program
Application Domains
Highlights of the Year
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]
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.
[2]
C. 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
[3]
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.
http://epubs.siam.org/toc/sjnaam/52/4
[4]
C. 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.
[5]
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.
[6]
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
[7]
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
[8]
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.
[9]
E. 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
[10]
E. 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

[11]
A. 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, in: ESAIM: Mathematical Modelling and Numerical Analysis, 2017, forthcoming. [ DOI : 10.1051/m2an/2017012 ]
https://hal.archives-ouvertes.fr/hal-01372954
[12]
B. Andreianov, C. Cancès, A. Moussa.
A nonlinear time compactness result and applications to discretization of degenerate parabolic-elliptic PDEs, in: Journal of Functional Analysis, 2017, vol. 273, no 12, pp. 3633-3670, https://arxiv.org/abs/1504.03891.
https://hal.archives-ouvertes.fr/hal-01142499
[13]
C. Besse, G. Dujardin, I. Lacroix-Violet.
High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates, in: SIAM Journal on Numerical Analysis, 2017, vol. 55, no 3, pp. 1387-1411, https://arxiv.org/abs/1507.00550.
https://hal.archives-ouvertes.fr/hal-01170888
[14]
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, September 2017, vol. 25, no 3, https://arxiv.org/abs/1601.00813.
https://hal.archives-ouvertes.fr/hal-01250709
[15]
F. Boyer, F. Nabet.
A DDFV method for a Cahn-Hilliard/Stokes phase field model with dynamic boundary conditions, in: ESAIM: Mathematical Modelling and Numerical Analysis, October 2017, vol. 51, no 5, pp. 1691-1731.
https://hal.archives-ouvertes.fr/hal-01249262
[16]
K. Brenner, C. Cancès.
Improving Newton's method performance by parametrization: the case of Richards equation, in: SIAM Journal on Numerical Analysis, 2017, vol. 55, no 4, pp. 1760–1785, https://arxiv.org/abs/1607.01508.
https://hal.archives-ouvertes.fr/hal-01342386
[17]
C. Calgaro, E. Creusé, T. Goudon, S. Krell.
Simulations of non homogeneous viscous flows with incompressibility constraints, in: Mathematics and Computers in Simulation, July 2017.
https://hal.archives-ouvertes.fr/hal-01246070
[18]
C. Calgaro, M. Ezzoug, E. Zahrouni.
Stability and convergence of an hybrid finite volume-finite element method for a multiphasic incompressible fluid model, in: Communications on Pure and Applied Analysis, March 2018, vol. 17, no 2, pp. 429-448.
https://hal.archives-ouvertes.fr/hal-01586201
[19]
C. Cancès, C. Chainais-Hillairet, S. Krell.
Numerical analysis of a nonlinear free-energy diminishing Discrete Duality Finite Volume scheme for convection diffusion equations, in: Computational Methods in Applied Mathematics, 2017, https://arxiv.org/abs/1705.10558 - Special issue on "Advanced numerical methods: recent developments, analysis and application", forthcoming. [ DOI : 10.1515/cmam-2017-0043 ]
https://hal.archives-ouvertes.fr/hal-01529143
[20]
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, https://arxiv.org/abs/1607.04009. [ DOI : 10.2140/apde.2017.10.1845 ]
https://hal.archives-ouvertes.fr/hal-01345438
[21]
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://arxiv.org/abs/1503.05649.
https://hal.archives-ouvertes.fr/hal-01119735
[22]
C. Cancès, M. Ibrahim, M. Saad.
Positive nonlinear CVFE scheme for degenerate anisotropic Keller-Segel system, in: SMAI Journal of Computational Mathematics, 2017, vol. 3, pp. 1–28.
https://hal.archives-ouvertes.fr/hal-01119210
[23]
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, 2017, https://arxiv.org/abs/1609.00519v1 - 27 pages, 8 figures, forthcoming. [ DOI : 10.1515/acv-2016-0034 ]
https://hal.archives-ouvertes.fr/hal-01359483
[24]
E. Creusé, S. Nicaise, R. Tittarelli.
A guaranteed equilibrated error estimator for the A − ϕ and T − Ω magnetodynamic harmonic formulations of the Maxwell system, in: IMA Journal of Numerical Analysis, 2017, vol. 37, no 2, pp. 750-773.
https://hal.archives-ouvertes.fr/hal-01110258
[25]
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
[26]
M. Goldman, B. Merlet.
Phase segregation for binary mixtures of Bose-Einstein Condensates, in: SIAM Journal on Mathematical Analysis / SIAM Journal of Mathematical Analysis, 2017, vol. 49, no 3, pp. 1947–1981, https://arxiv.org/abs/1505.07234. [ DOI : 10.1137/15M1051105 ]
https://hal.archives-ouvertes.fr/hal-01155676
[27]
P.-E. Jabin, T. Rey.
Hydrodynamic limit of granular gases to pressureless Euler in dimension 1, in: Quarterly of Applied Mathematics, 2017, vol. 75, pp. 155-179, https://arxiv.org/abs/1602.09103 - 26 pages, 1 figure. [ DOI : 10.1090/qam/1442 ]
https://hal.archives-ouvertes.fr/hal-01279961
[28]
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, 2017, https://arxiv.org/abs/1607.06646, forthcoming.
https://hal.archives-ouvertes.fr/hal-01347943
[29]
L. Pareschi, T. Rey.
Residual equilibrium schemes for time dependent partial differential equations, in: Computers and Fluids, October 2017, https://arxiv.org/abs/1602.02711 - 23 pages, 12 figures. [ DOI : 10.1016/j.compfluid.2017.07.013 ]
https://hal.archives-ouvertes.fr/hal-01270297
[30]
R. Tittarelli, Y. Le Menach, F. Piriou, E. Creusé, S. Nicaise, J.-P. Ducreux.
Comparison of Numerical Error Estimators for Eddy Current Problems solved by FEM, in: IEEE Transactions on Magnetics, 2017, forthcoming.
https://hal.archives-ouvertes.fr/hal-01645591

International Conferences with Proceedings

[31]
A. Ait Hammou Oulhaj.
A finite volume scheme for a seawater intrusion model with cross-diffusion, in: FVCA8 2017 - International Conference on Finite Volumes for Complex Applications 8, Lille, France, June 2017, pp. 421-429. [ DOI : 10.1007/978-3-319-57397-7_35 ]
https://hal.archives-ouvertes.fr/hal-01541229
[32]
C. Cancès, C. Chainais-Hillairet, S. Krell.
A nonlinear Discrete Duality Finite Volume Scheme for convection-diffusion equations, in: FVCA8 2017 - International Conference on Finite Volumes for Complex Applications VIII, Lille, France, C. Cancès, P. Omnes (editors), Springer Proceedings in Mathematics & Statistics, Springer International Publishing, 2017, vol. 199, pp. 439-447.
https://hal.archives-ouvertes.fr/hal-01468811
[33]
C. Cancès, D. Granjeon, N. Peton, Q. H. Tran, S. Wolf.
Numerical scheme for a stratigraphic model with erosion constraint and nonlinear gravity flux, in: FVCA 8 - 2017 - International Conference on Finite Volumes for Complex Applications VIII, Lille, France, Proceedings in Mathematics & Statistics, Springer, June 2017, vol. 200, pp. 327-335. [ DOI : 10.1007/978-3-319-57394-6_35 ]
https://hal.archives-ouvertes.fr/hal-01639681
[34]
C. Chainais-Hillairet, B. Merlet, A. Zurek.
Design and analysis of a finite volume scheme for a concrete carbonation model, in: FVCA8 2017 - International Conference on Finite Volumes for Complex Applications VIII, Lille, France, Springer Proceedings in Mathematics & Statistics, June 2017, vol. 199, pp. 285-292. [ DOI : 10.1007/978-3-319-57397-7_21 ]
https://hal.archives-ouvertes.fr/hal-01645137

Conferences without Proceedings

[35]
M. Bessemoulin-Chatard, C. Chainais-Hillairet, A. Jüngel.
Uniform L ∞ estimates for approximate solutions of the bipolar drift-diffusion system, in: FVCA 8, Lille, France, June 2017, https://arxiv.org/abs/1702.06300.
https://hal.archives-ouvertes.fr/hal-01472643
[36]
C. Calgaro, M. Ezzoug.
L-Stability of IMEX-BDF2 Finite Volume Scheme for Convection-Diffusion Equation, in: FVCA 2017: Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects, Lille, France, C. Cancès, P. Omnes (editors), Springer Proceedings in Mathematics & Statistics, Springer, June 2017, vol. 199, pp. 245-253. [ DOI : 10.1007/978-3-319-57397-7_17 ]
https://hal.archives-ouvertes.fr/hal-01574893
[37]
C. Cancès, F. Nabet.
Finite volume approximation of a degenerate immiscible two-phase flowmodel of Cahn-Hilliard type, in: FVCA8 2017 - International Conference on Finite Volumes for Complex Applications VIII, Lille, France, Springer Proceedings in Mathematics and Statistics, 2017, vol. 199, pp. 431-438.
https://hal.archives-ouvertes.fr/hal-01468795
[38]
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
[39]
W. Melis, T. Rey, G. Samaey.
Projective integration for nonlinear BGK kinetic equations, in: Finite Volumes for Complex Applications VIII, Lille, France, C. Cancès, P. Omnès (editors), Hyperbolic, Elliptic and Parabolic Problems, Springer International Publishing, June 2017, vol. 200, pp. 155-162, https://arxiv.org/abs/1702.00563 - Proceedings FVCA 8. [ DOI : 10.1007/978-3-319-57394-6 ]
https://hal.archives-ouvertes.fr/hal-01451580

Scientific Books (or Scientific Book chapters)

[40]
C. Cancès, P. Omnes (editors)
Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, Springer Proceedings in Mathematics & Statistics, Springer, France, 2017, vol. 200.
https://hal.archives-ouvertes.fr/hal-01639713
[41]
C. Cancès, P. Omnes (editors)
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects: FVCA 8, Lille, France, June 2017, Springer Proceedings in Mathematics & Statistics, Springer International Publishing, France, 2017, vol. 199.
https://hal.archives-ouvertes.fr/hal-01639725

Other Publications

[42]
A. 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. [ DOI : 10.1002/num.22234 ]
https://hal.archives-ouvertes.fr/hal-01432197
[43]
M. Bessemoulin-Chatard, C. Chainais-Hillairet.
Uniform-in-time Bounds for approximate Solutions of the drift-diffusion System, December 2017, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01659418
[44]
D. Bresch, M. Gisclon, I. Lacroix-Violet.
On Navier-Stokes-Korteweg and Euler-Korteweg Systems: Application to Quantum Fluids Models, March 2017, https://arxiv.org/abs/1703.09460 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01496960
[45]
C. Calgaro, C. Colin, E. Creusé.
A combined Finite Volumes -Finite Elements method for a low-Mach model: Application to the simulation of a transient injection flow, August 2017, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01574894
[46]
C. Cancès, D. Matthes, F. Nabet.
A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow, December 2017, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01665338
[47]
C. Chainais-Hillairet, B. Merlet, A. Zurek.
Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation, February 2017, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01477543
[48]
A. Chambolle, L. A. D. Ferrari, B. Merlet.
Variational approximation of size-mass energies for k-dimensional currents, October 2017, https://arxiv.org/abs/1710.08808 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01622540
[49]
M. Goldman, B. Merlet, V. Millot.
A Ginzburg-Landau model with topologically induced free discontinuities, November 2017, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01643795
[50]
W. Melis, T. Rey, G. Samaey.
Projective and telescopic projective integration for the nonlinear BGK and Boltzmann equations, December 2017, https://arxiv.org/abs/1712.06362 - 35 pages, 2 annexes, 12 figures.
https://hal.archives-ouvertes.fr/hal-01666346
References in notes
[51]
R. 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
[52]
R. 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
[53]
R. 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
[54]
R. 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
[55]
T. Aiki, A. Muntean.
Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structure, in: Adv. Math. Sci. Appl., 2009, vol. 19, pp. 109-129.
[56]
T. 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
[57]
B. 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
[58]
M. Avila, J. Principe, R. Codina.
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. [ DOI : 10.1016/j.jcp.2011.06.032 ]
[59]
I. Babuška, W. C. Rheinboldt.
Error estimates for adaptive finite element computations, in: SIAM J. Numer. Anal., 1978, vol. 15, no 4, pp. 736–754.
[60]
J. Bear, Y. Bachmat.
Introduction to modeling of transport phenomena in porous media, Springer, 1990, vol. 4.
[61]
J. Bear.
Dynamic of Fluids in Porous Media, American Elsevier, New York, 1972.
[62]
A. Beccantini, E. Studer, S. Gounand, J.-P. Magnaud, T. Kloczko, C. Corre, S. Kudriakov.
Numerical simulations of a transient injection flow at low Mach number regime, in: Internat. J. Numer. Methods Engrg., 2008, vol. 76, no 5, pp. 662–696. [ DOI : 10.1002/nme.2331 ]
[63]
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.
http://dx.doi.org/10.1016/j.compfluid.2010.08.014
[64]
D. 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.
[65]
D. Bresch, P. Noble, J.-P. Vila.
Relative entropy for compressible Navier-Stokes equations with density dependent viscosities and various applications, 2017, To appear in ESAIM Proc..
[66]
C. 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
[67]
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
[68]
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
[69]
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.
https://hal.archives-ouvertes.fr/hal-00924282
[70]
E. 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.
[71]
E. 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
[72]
D. 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).
[73]
V. 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
[74]
D. Donatelli, E. Feireisl, P. Marcati.
Well/ill posedness for the Euler-Korteweg-Poisson system and related problems, in: Comm. Partial Differential Equations, 2015, vol. 40, pp. 1314-1335.
[75]
J. 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.
[76]
W. E, P. Palffy-Muhoray.
Phase separation in incompressible systems, in: Phys. Rev. E, Apr 1997, vol. 55, pp. R3844–R3846.
https://link.aps.org/doi/10.1103/PhysRevE.55.R3844
[77]
C. M. Elliott, H. Garcke.
On the Cahn-Hilliard equation with degenerate mobility, in: SIAM J. Math. Anal., 1996, vol. 27, no 2, pp. 404–423.
http://dx.doi.org/10.1137/S0036141094267662
[78]
E. 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.
[79]
R. 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
[80]
J. Giesselmann, C. Lattanzio, A.-E. Tzavaras.
Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics, in: Arch. Rational Mech. Analysis, 2017, vol. 223, pp. 1427-1484.
[81]
V. Gravemeier, W. A. Wall.
Residual-based variational multiscale methods for laminar, transitional and turbulent variable-density flow at low Mach number, in: Internat. J. Numer. Methods Fluids, 2011, vol. 65, no 10, pp. 1260–1278. [ DOI : 10.1002/fld.2242 ]
[82]
L. 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
[83]
F. 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
[84]
M. 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
[85]
S. Jin.
Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations, in: SIAM, J. Sci. Comput., 1999, vol. 21, pp. 441-454.
[86]
R. 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.
[87]
A. 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.
[88]
C. 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
[89]
F. Otto, W. E.
Thermodynamically driven incompressible fluid mixtures, in: J. Chem. Phys., 1997, vol. 107, no 23, pp. 10177-10184.
https://doi.org/10.1063/1.474153
[90]
F. 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.
[91]
M. 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
[92]
D. Ruppel, E. Sackmann.
On defects in different phases of two-dimensional lipid bilayers, in: J. Phys. France, 1983, vol. 44, no 9, pp. 1025-1034.
http://dx.doi.org/10.1051/jphys:019830044090102500
[93]
F. 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
[94]
C. 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
[95]
M. 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
[96]
J. 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
[97]
P. G. de Gennes.
Dynamics of fluctuations and spinodal decomposition in polymer blends, in: J. Chem. Phys., 1980, vol. 72, pp. 4756-4763.