Preprints


C. Cancès, J. Venel. On the square-root approximation finite volume scheme for nonlinear drift-diffusion equations. HAL: hal-03693887, 2022 (pdf).

C. Cancès, C. Chainais-Hillairet, B. Merlet, F. Raimondi, J. Venel. Mathematical analysis of a thermodynamically consistent reduced model for iron corrosion. HAL: hal-03549457, 2022 (pdf).

C. Cancès, V. Ehrlacher, L. Monasse. Finite Volumes for the Stefan-Maxwell cross-diffusion system.
HAL: hal-02902672, 2020 (pdf).

C. Cancès, D. Matthes. Construction of a two-phase flow with singular energy by gradient flow methods.
HAL: hal-02510535, 2020 (pdf).



Articles in international journals


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., to appear (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).

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).

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).

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, 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).

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, 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).

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)

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)

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, 2010 (pdf).

O. Blondel, C. Cancès, M. Sasada, M. Simon. Convergence of a degenerate microscopic dynamics to the porous medium equation, arXiv:1802.05912 (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)


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).