Preprints
J.
W. Both, C. Cancès. A global existence result for weakly coupled
two-phase poromechanics.
HAL: hal-04316962, 2023 (pdf).
I.
Ben Gharbia, C. Cancès, T. Faney, M. Jonval, Q.-H.
Tran. Robust resolution of single-phase chemical equilibrium
using parametrization and Cartesian representation techniques. HAL:
hal-04225504, 2023 (pdf).
C. Cancès, D.
Matthes, F.
Nabet, E.-M. Rott. Finite elements for Wasserstein $W_p$
gradient flows.
HAL:hal-03719189, 2022 (pdf).
Articles in international journals
C.
Calgaro, C. Cancès, E.
Creusé. Discrete Gagliardo-Nirenberg inequality and application
to the finite volume approximation of a convection-diffusion equation
with a Joule effect term. Accepted for publication in IMA J. Numer.
Anal. (pdf)
C. Cancès, V.
Ehrlacher, L.
Monasse. Finite Volumes for the Stefan-Maxwell cross-diffusion
system.
IMA J. Numer. Anal, DOI:
10.1093/imanum/drad032, 2023 (pdf).
C. Cancès, C.
Chainais-Hillairet, B.
Merlet, F. Raimondi, J.
Venel. Mathematical analysis of a thermodynamically consistent
reduced model for iron corrosion. Z. Angew. Math. Phys. 74:96, 2023
(pdf).
C. Cancès, J.
Venel. On the square-root approximation finite volume scheme
for nonlinear drift-diffusion equations. Comptes Rendus
Mathématiques, 361, pp.535-558, 2023, (pdf).
C. Cancès, D. Matthes. Construction of a two-phase flow with singular energy by gradient flow methods.
S. Bassetto, C. Cancès, G. Enchéry, Q.
H. Tran. On several numerical strategies to solve Richards’
equation in heterogeneous media with Finite Volumes. Comput. Geosci.,
26, pp. 1297-1322, 2022 (pdf).
C. Cancès, A.
Zurek. A convergent finite volume scheme for dissipation driven
models with volume filling constraint. Numer. Math., 151, pp.
279-328, 2022 (pdf).
S. Bassetto, C. Cancès, G. Enchéry, Q.
H. Tran. Upstream mobility Finite Volumes for the Richards
equation in heterogeneous domains. ESAIM Math. Model. Numer. Anal.,
55(5), pp. 2101-2139, 2021 (pdf).
C. Cancès, F.
Nabet. Finite Volume approximation of a two-phase two fluxes
degenerate Cahn-Hilliard model.
ESAIM Math. Model. Numer. Anal., 55(3), pp. 969-1003, 2021 (pdf).
ESAIM Math. Model. Numer. Anal., 55(3), pp. 969-1003, 2021 (pdf).
C. Cancès, D. Maltese. A gravity current
model with capillary trapping for oil migration in multilayer
geological basins. SIAM J. Appl. Math., 81(2), pp. 454-484, 2021 (pdf).
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. IMA J. Numer. Anal., 41(1), pp. 271-314, 2021 (pdf).
C. Cancès, F.
Nabet, M.
Vohralik. Convergence and a posteriori error analysis for
energy-stable finite element approximations of degenerate parabolic
equations. Math. Comp., 90, pp. 517-563, 2021 (pdf).
C. Cancès, T.
O. Gallouët, G. Todeschi. A variational finite volume scheme
for Wasserstein gradient flows.
Numer. Math., 146(3), pp. 437-480, 2020 (pdf).
Numer. Math., 146(3), pp. 437-480, 2020 (pdf).
C. Cancès, B.
Gaudeul. A convergent entropy diminishing finite volume scheme
for a cross-diffusion system.
SIAM J. Numer. Anal., 58(5), pp.
2684-2710, 2020 (pdf).
C. Cancès,C.
Chainais-Hillairet, M.Herda,
S. Krell. Large time
behavior of nonlinear finite volume schemes for convection-diffusion
equations. SIAM J. Numer. Anal., 58(5), pp. 2544-2571, 2020 (pdf).
N. Peton, C. Cancès, D.
Granjeon, Q.-H.
Tran, S. Wolf. Numerical scheme for a water flow-driven forward
stratigraphic model. Comput. Geosci, 24, pp. 37-60, 2020 (pdf).
A. Ait Hammou Oulhaj, C. Cancès, C.
Chainais-Hillairet, P.
Laurençot. Large time behavior of a two phase extension of the
porous medium equation, Interfaces Free Bound., 21, pp. 199-229, 2019
(pdf).
C. Cancès, D.Matthes,
F. Nabet. A
two-phase two-fluxes degenerate Cahn-Hilliard model as constrained
Wasserstein gradient flow, Arch. Rational Mech. Anal., 233(2), pp.
837-866, 2019 (pdf).
C. Cancès, T.
O. Gallouët, M.
Laborde, L.
Monsaingeon. Simulation of multiphase porous media flows with
minimizing movement and finite volume schemes, European J. Appl. Math,
30(6), pp. 1123-1152, 2019 (pdf).
C. Cancès, C.
Chainais-Hillairet, A. Gerstenmayer, A.
Jüngel. Convergence of a Finite-Volume scheme for a degenerate
cross-diffusion model for ion transport, Numer. Meth. Partial
Differential Equations, 35(2), pp. 545-575, 2019 (pdf).
C. Cancès. Energy stable numerical methods for porous media flow type problems, Oil & Gas Science and Technology - Revue de l’IFP Énergies Nouvelles, 73(78), pp. 1-18, 2018 (pdf)
C. Cancès, C. Chainais-Hillairet, S. Krell. Numerical analysis of a nonlinear free-energy diminishing Discrete Duality Finite Volume scheme for convection diffusion equations. Comput. Methods Appl. Math., 18(3), pp. 407-432, 2018 (pdf).
C. Cancès. Energy stable numerical methods for porous media flow type problems, Oil & Gas Science and Technology - Revue de l’IFP Énergies Nouvelles, 73(78), pp. 1-18, 2018 (pdf)
C. Cancès, C. Chainais-Hillairet, S. Krell. Numerical analysis of a nonlinear free-energy diminishing Discrete Duality Finite Volume scheme for convection diffusion equations. Comput. Methods Appl. Math., 18(3), pp. 407-432, 2018 (pdf).
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, ESAIM Math. Model. Numer. Anal., 2018, 52(4), pp. 1532-1567 (pdf).
B. Andreianov, C. Cancès, A. Moussa. A nonlinear time compactness result and applications to discretization of degenerate parabolic-elliptic PDEs, J. Funct. Anal., 2017, 273(12), pp. 3633-3670 (pdf).
C. Cancès, T.
O. Gallouët, L.
Monsaingeon. Incompressible immiscible multiphase flows in
porous media: a variational approach, Analysis & PDE, 2017, 10(8),
pp. 1845-1876 (pdf).
K.
Brenner, Cancès. Improving Newton's method performance by
parametrization: the case of Richards equation, SIAM J. Numer. Anal.,
2017, 55(4), pp. 1760-1785 (pdf).
C. Cancès, M. Ibrahim, M.
Saad. Positive nonlinear CVFE scheme for degenerate anisotropic
Keller-Segel system, SMAI-JCM, 2017, 3, pp. 1-28 (pdf).
C. Cancès, C. Guichard. Numerical analysis of a robust free energy diminishing finite volume scheme for degenerate parabolic equations with gradient structure, Found. Comput. Math, 2017, 17(6), pp. 1525-1584 (pdf).
C. Cancès, C. Guichard. Numerical analysis of a robust free energy diminishing finite volume scheme for degenerate parabolic equations with gradient structure, Found. Comput. Math, 2017, 17(6), pp. 1525-1584 (pdf).
C. Cancès, H.
Mathis, N. Seguin.
Error estimate for time-explicit finite volume approximation of strong
solutions to systems of conservation laws, SIAM J. Numer. Anal., 2016,
54(2), pp. 1263-1287 (pdf).
C. Cancès, C.
Guichard. Convergence of a nonlinear entropy diminishing Control
Volume Finite Element scheme for solving anisotropic degenerate
parabolic equations. Math. Comp., 2016, 85(298), pp. 549-580 (pdf).
C. Cancès, F. Coquel, E.
Godlewski, H.
Mathis, N. Seguin.
Error analysis of a dynamic model adaptation procedure for nonlinear
hyperbolic equations. Comm. Math. Sci., 2016, 14(1), pp. 1-30 (pdf).
C. Cancès, T.
O. Gallouët, L.
Monsaingeon. The gradient flow structure for incompressible
immiscible two-phase flows in porous media, C. R. Acad. Sci. Paris,
Série I, 2015, 353, pp. 985-989 (pdf).
B.
Andreianov, C. Cancès. On interface transmission conditions for
conservation laws with discontinuous flux of general shape. J. Hyp.
Diff. Eq., 2015, 12(2), pp. 343-384 (pdf).
H.
Mathis, C. Cancès, E. Godlewski, N.
Seguin, Dynamic model adaptation for multiscale simulation of
hyperbolic systems with relaxation, J. Sci. Comput., 2015, 63(3), pp.
820-861 (pdf).
B.
Andreianov, C. Cancès. A phase-by-phase upstream scheme that
converges to the vanishing capillarity solution for countercurrent
two-phase flow in two-rocks media. Comput. Goesci., 2014, 18(2), pp.
211-226 (pdf).
C. Cancès, I.S.
Pop, M.
Vohralik, An a posteriori error estimate for vertex-centered
finite volume discretizations of immiscible incompressible two-phase
flow, Math. Comp., 2014, 83(285), pp. 153-188 (pdf).
B.
Andreianov, K.
Brenner, C. Cancès, Approximating the vanishing capillarity
limit of two-phase flow in multi-dimensional heterogeneous porous
medium, ZAMM Z. Angew. Math. Mech., 2014, 94(7-8), pp. 651-667 (pdf).
C. Cancès, M. Cathala, Ch. Le Potier,
Monotone coercive cell-centered finite volume schemes for anisotropic
diffusion equations, Numer. Math., 2013, 125(3), pp. 387-417 (pdf).
K.
Brenner, C. Cancès, D.
Hilhorst, Finite volume approximation for an immiscible
two-phase flow in porous media with discontinuous capillary pressure,
Comput. Geosci., 2013, 17(3), pp. 573-597 (pdf).
B. Andreianov, C. Cancès, Vanishing capillarity solutions of Buckley-Leverett equation with gravity in two-rocks’ medium, Comput. Geosci., 2013, 17(3), pp. 551-572 (pdf).
B. Andreianov, C. Cancès, Vanishing capillarity solutions of Buckley-Leverett equation with gravity in two-rocks’ medium, Comput. Geosci., 2013, 17(3), pp. 551-572 (pdf).
C. Cancès, N.
Seguin, Error estimate for Godunov approximation of locally
constrained conservation laws, SIAM J. Numer. Anal., 2012, 50(6), pp.
3036–3060 (pdf).
C. Cancès, M. Pierre, An existence result
for multidimensional immiscible two-phase flows with discontinuous
capillary pressure field, SIAM J. Math. Anal.,2012, 44(2), pp.
966-992 (pdf).
B.
Andreianov, C. Cancès, The Godunov scheme for scalar
conservation laws with discontinuous bell-shaped flux functions, Appl.
Math. Letters, 2012, 25, pp. 1844-1848 (pdf).
C. Cancès, T.
Gallouët. On the time continuity of entropy solutions, J. Evol.
Equ., 2011, 11 (1), pp. 43-55 (pdf).
C. Cancès. On the effects of discontinuous capillarities for immiscible two-phase flows in porous media made of several rock-types, Networks Het. Media, 2010, 5 (3), pp. 635-647 (pdf).
C. Cancès. Asymptotic behavior of
two-phase flows in heterogeneous porous media for capillarity
depending only on space. I. Convergence to the optimal entropy
solution, SIAM J. Math. Anal., 2010, 42 (2), pp. 946-971 (pdf).
C. Cancès. Asymptotic behavior of
two-phase flows in heterogeneous porous media for capillarity
depending only on space. II. Non-classical shocks to model
oil-trapping, SIAM J. Math. Anal., 2010, 42 (2), pp. 972-995 (pdf).
C. Cancès. Finite volume scheme for
two-phase flow in heterogeneous porous media involving capillary
pressure discontinuities, M2AN Math. Model. Numer. Anal., 2009, 43,
973-1001 (pdf).
C. Cancès, T.
Gallouët, A.
Porretta. Two-phase flows involving capillary barriers in
heterogeneous porous media, Interfaces and Free Bound., 2009, 11, pp
239-258 (pdf).
C. Cancès. Nonlinear parabolic equation
with spatial discontinuities, NoDEA Nonlinear Differential Equations
Appl., 2008, 15, pp 427-456 (pdf).
Conference papers and book chapters
C. Cancès, M.
Herda, A.
Massimini. Finite volumes for a generalized
Poisson-Nernst-Planck system with cross-diffusion and size exclusion.
FVCA10 - International Conference on Finite Volumes for Complex
Applications X, 2023, Strasbourg, France (pdf)
C. Cancès, J.
Cauvin-Vila, C.
Chainais-Hillairet, V.
Ehrlacher. Structure Preserving Finite Volume Approximation of
Cross-Diffusion Systems Coupled by a Free Interface. FVCA10 -
International Conference on Finite Volumes for Complex Applications X,
2023, Strasbourg, France (pdf)
C. Cancès, J.
Droniou, C.
Guichard, G. Manzini, M.
Bastidas Olivares, I.
S. Pop.
Error estimates for the gradient discretisation of degenerate parabolic equation of porous medium type.
SEMA-SIMAI volume "Polyhedral methods in geosciences" (pdf).
Error estimates for the gradient discretisation of degenerate parabolic equation of porous medium type.
SEMA-SIMAI volume "Polyhedral methods in geosciences" (pdf).
C. Cancès, F.
Nabet. Energy stable discretization of two-phase porous media
flows. FVCA9 - International Conference on Finite Volumes for Complex
Applications IX, 2020, Bergen, Norway (pdf)
C. Cancès, B. Gaudeul. Entropy
diminishing finite volume approximation of a cross-diffusion system.
FVCA9 - International Conference on
Finite Volumes for Complex Applications IX, 2020, Bergen, Norway (pdf).
C. Cancès, C. Chainais-Hillairet, J.
Fuhrmann, B. Gaudeul. On four numerical schemes for a unipolar
degenerate drift-diffusion model. FVCA9 - International Conference on
Finite Volumes for Complex Applications IX, 2020, Bergen, Norway (pdf).
S. Bassetto, C. Cancès, G. Enchéry, Q.-H.
Tran. Robust Newton solver based on variable switch for a finite
volume discretization of Richards equation. FVCA9 - International
Conference on Finite Volumes for Complex Applications IX, 2020,
Bergen, Norway (pdf).
C. Cancès, F.
Nabet. Finite volume approximation of a degenerate immiscible
two-phase flow model of Cahn-Hilliard type. FVCA8 - International
Conference on Finite Volumes for Complex Applications VIII, 2017,
Lille, France.
Springer Proceedings in Mathematics and Statistics 199, pp.431-438, 2017 (pdf)
C. Cancès, C. Chainais-Hillairet, S. Krell. A nonlinear Discrete Duality Finite Volume Scheme for convection-diffusion equations. FVCA8 - International Conference on Finite Volumes for Complex Applications VIII, 2017, Lille, France.
Springer Proceedings in Mathematics and Statistics 199, pp.439-447, 2017 (pdf)
Springer Proceedings in Mathematics and Statistics 199, pp.431-438, 2017 (pdf)
C. Cancès, C. Chainais-Hillairet, S. Krell. A nonlinear Discrete Duality Finite Volume Scheme for convection-diffusion equations. FVCA8 - International Conference on Finite Volumes for Complex Applications VIII, 2017, Lille, France.
Springer Proceedings in Mathematics and Statistics 199, pp.439-447, 2017 (pdf)
Cancès C., Ibrahim M., Saad
M. A Nonlinear CVFE Scheme for an Anisotropic Degenerate
Nonlinear Keller-Segel Model. In: Russo G., Capasso V., Nicosia G.,
Romano V. (eds) Progress in Industrial Mathematics at ECMI 2014.
Mathematics in Industry, vol 22. Springer, Cham, 2016 (link)
C. Cancès, C.
Guichard. Entropy-diminishing CVFE scheme for solving
anisotropic degenerate diffusion equations. FVCA7 conference
proceedings, 2014. (pdf).
A.-C.
Boulanger, C. Cancès, H.
Mathis, K. Saleh,
N. Seguin. OSAMOAL:
optimized simulations by adapted models using asymptotic limits, ESAIM
Proceedings, 2012, 38, pp. 183-201 (pdf).
C. Cancès, C. Choquet, Y. Fan, I.S. Pop, An existence result related to two-phase flows with dynamic capillary pressure, MAMERN, 2011 (pdf)
C. Cancès, C. Choquet, Y. Fan, I.S. Pop, An existence result related to two-phase flows with dynamic capillary pressure, MAMERN, 2011 (pdf)
K.
Brenner, C. Cancès, D.
Hilhorst, A Convergent Finite Volume Scheme forTwo-Phase Flows
in Porous Media with Discontinuous Capillary Pressure Field, Finite
volumes for complex applications VI, 2011 (pdf).
C. Cancès. Two-phase Flows Involving Discontinuities on the Capillary Pressure, Finite volumes for complex applications V: problems and perspectives; Robert Eymard and Jean-Marc Hérard (Eds), Hermes, 2008 (pdf)
Edited books
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects, C. Cancès and P. Omnes (Eds), Springer Proceedings in Mathematics and Statistics, vol. 199, 2017 (doi : 10.1007/978-3-319-57397-7)
Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, C. Cancès and P. Omnes (Eds), Springer Proceedings in Mathematics and Statistics, vol. 200, 2017 (doi: 10.1007/978-3-319-57394-6)
Research reports
C. Cancès, C. Choquet, Y. Fan, I.S. Pop, Existence of weak solutions to a degenerate pseudo-parabolic equation modeling two-phase flow in porous media, CASA-Report 10-75 (pdf).
O.
Blondel, C. Cancès, M. Sasada, M.
Simon. Convergence of a degenerate microscopic dynamics to the
porous medium equation, arXiv:1802.05912 (pdf).
C. Cancès, C.
Chainais-Hillairet, B. Merlet, F. Raimondi, J.
Venel. Thermodynamically consistent modelling of the corrosion
of iron in the context of deep subsurface nuclear waste repositories,
HAL: hal-04210782 (pdf).
Other reports
Ahusborde, E., Amaziane, B., Baksay, A.,
Bátor, G., Becker, D., Bednár, A., Béres, M., Blaheta, R., Böhti, Z.,
Bracke, G. , Brazda,
L., Brendler, V., Brenner, K., Brezina, J., Cancès, C., Chainais-Hillairet, C. , Chave, F. , Claret, F., Domesová, S., Havlova, V.,
Hokr, M., Horák, D., Jacques, D., Jankovsky, F. Kazymyrenko, C.,Kolditz, O., Koudelka, T., Kovács, T., Krejci, T., Kruis, J.,
Laloy, E., Landa, J., Lipping, T., Lukin, D., Masin,D., Masson, R., Meeussen, J.C.L, Mollaali, M., Mon, A., Montenegro, L.,
Montoya, V., Pepin, G., Poonoosamy,J., Prasianakis, N., Saâdi, Z., Samper, J., Scaringi,G., Sochala, P., Tournassat, C.,
Yoshioka, K., Yuankai, Y.. (2021): State Of the Art Report in the fields of numerical analysis and scientific computing. Final
version as of 16/02/2020 of deliverable D4.1 of the HORIZON 2020 project EURAD. EC Grant agreement no: 847593 (pdf)
L., Brendler, V., Brenner, K., Brezina, J., Cancès, C., Chainais-Hillairet, C. , Chave, F. , Claret, F., Domesová, S., Havlova, V.,
Hokr, M., Horák, D., Jacques, D., Jankovsky, F. Kazymyrenko, C.,Kolditz, O., Koudelka, T., Kovács, T., Krejci, T., Kruis, J.,
Laloy, E., Landa, J., Lipping, T., Lukin, D., Masin,D., Masson, R., Meeussen, J.C.L, Mollaali, M., Mon, A., Montenegro, L.,
Montoya, V., Pepin, G., Poonoosamy,J., Prasianakis, N., Saâdi, Z., Samper, J., Scaringi,G., Sochala, P., Tournassat, C.,
Yoshioka, K., Yuankai, Y.. (2021): State Of the Art Report in the fields of numerical analysis and scientific computing. Final
version as of 16/02/2020 of deliverable D4.1 of the HORIZON 2020 project EURAD. EC Grant agreement no: 847593 (pdf)
Theses
Analyse mathématique et numérique d'équations aux dérivées partielles issues de la mécanique des fluides : applications aux écoulements en milieux poreux, Habilitation Thesis, UPMC Paris 6, 2015 (pdf).
Two-phase flows in heterogeneous porous
media : modeling and analysis of the flows of the effects involved by
the discontinuities of the capillary pressure, PhD Thesis, Université
de Provence, 2008 (pdf).
