Open Access
Issue
ESAIM: M2AN
Volume 55, Number 3, May-June 2021
Page(s) 969 - 1003
DOI https://doi.org/10.1051/m2an/2021002
Published online 05 May 2021
  1. L. Ambrosio, N. Gigli and G. Savaré, Gradient flows in metric spaces and in the space of probability measures, 2nd edition. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel (2008). [Google Scholar]
  2. B. Andreianov, Time compactness tools for discretized evolution equations and applications to degenerate parabolic PDEs, edited by J. Fořt, J. Fürst, J. Halama, R. Herbin and F. Hubert. In: Finite Volumes for Complex Applications. VI. Problems & Perspectives. Springer Proceedings in Mathematics. Springer, Berlin, Heidelberg (2011) 21–29. [Google Scholar]
  3. B. Andreianov, C. Cancès and A. Moussa, A nonlinear time compactness result and applications to discretization of degenerate parabolic-elliptic PDEs. J. Funct. Anal. 273 (2017) 3633–3670. [Google Scholar]
  4. J.-D. Benamou, Y. Brenier and K. Guittet, Numerical analysis of a multi-phasic mass transport problem. In: Recent Advances in the Theory and Applications of Mass Transport. Vol. 353 of Contemporary Mathematics Amer. Math. Soc., Providence, RI (2004) 1–17. [Google Scholar]
  5. M. Bessemoulin-Chatard, C. Chainais-Hillairet and F. Filbet, On discrete functional inequalities for some finite volume schemes. IMA J. Numer. Anal. 35 (2015) 1125–1149. [Google Scholar]
  6. C. Cancès and C. Guichard, Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure. Found. Comput. Math. 17 (2017) 1525–1584. [Google Scholar]
  7. C. Cancès and D. Matthes, Construction of a two-phase flow with singular energy by gradient flow methods. HAL: hal-02510535 (2020). [Google Scholar]
  8. C. Cancès, D. Matthes and F. Nabet, A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow. Arch. Ration. Mech. Anal. 233 (2019) 837–866. [Google Scholar]
  9. C. Cancès and F. Nabet, Finite volume approximation of a degenerate immiscible two-phase flow model of Cahn-Hilliard type, In: Finite Volumes for Complex Applications VIII –Methods and Theoretical Aspects: edited by C. Cancès and P. Omnes. FVCA 8, Lille, France, June 2017. number 199 in Proceedings in Mathematics and Statistics. Springer International Publishing, Cham (2017) 431–438. [Google Scholar]
  10. C. Chainais-Hillairet, J.-G. Liu and Y.-J. Peng, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. ESAIM: M2AN 37 (2003) 319–338. [EDP Sciences] [Google Scholar]
  11. X. Chen, A. Jüngel and J.-G. Liu, A note on Aubin-Lions-Dubinskii lemmas. Acta Appl. Math. 133 (2013) 33–43. [Google Scholar]
  12. K. Deimling, Nonlinear Functional Analysis. Springer-Verlag, Berlin (1985). [Google Scholar]
  13. J. Droniou, R. Eymard, T. Gallouët, C. Guichard and R. Herbin, The Gradient Discretisation Method. In: Vol. 42 of Mathématiques et Applications. Springer International Publishing (2018). [Google Scholar]
  14. C.M. Elliott and H. Garcke, On the Cahn-Hilliard equation with degenerate mobility. SIAM J. Math. Anal. 27 (1996) 404–423. [Google Scholar]
  15. R. Eymard and T. Gallouët, H-convergence and numerical schemes for elliptic problems. SIAM J. Numer. Anal. 41 (2003) 539–562. [Google Scholar]
  16. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods. In: Handbook of numerical analysis. edited by P.G. Ciarlet, et al. North-Holland, Amsterdam (2000) 713–1020. [Google Scholar]
  17. R. Eymard, T. Gallouët and R. Herbin, Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes sushi: a scheme using stabilization and hybrid interfaces. IMA J. Numer. Anal. 30 (2010) 1009–1043. [Google Scholar]
  18. T. Gallouët, Discrete functional analysis tools for some evolution equations. Comput. Methods Appl. Math. 18 (2018) 477–493. [Google Scholar]
  19. T. Gallouët and J.-C. Latché, Compactness of discrete approximate solutions to parabolic PDEs – application to a turbulence model Comm. Pure Appl. Anal. 11 (2012) 2371–2391. [Google Scholar]
  20. P. Gladbach, E. Kopfer and J. Maas, Scaling limits of discrete optimal transport. SIAM J. Math. Anal. 52 (2020) 2759–2802. [Google Scholar]
  21. A. Glitzky and J.A. Griepentrog, Discrete Sobolev-Poincaré inequalities for Voronoi finite volume approximations. SIAM J. Numer. Anal. 48 (2010) 372–391. [Google Scholar]
  22. G. Grün and M. Rumpf, Nonnegativity preserving convergent schemes for the thin film equation. Numer. Math. 87 (2000) 113–152. [Google Scholar]
  23. R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1–17. [Google Scholar]
  24. J. Leray and J. Schauder, Topologie et équations fonctionnelles. Ann. Sci. École Norm. Sup. 51 (1934) 45–78. [Google Scholar]
  25. S. Lisini, D. Matthes and G. Savaré, Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. J. Differ. Equ. 253 (2012) 814–850. [Google Scholar]
  26. J. Maas, Gradient flows of the entropy for finite Markov chains. J. Funct. Anal. 261 (2011) 2250–2292. [Google Scholar]
  27. J. Maas and D. Matthes, Long-time behavior of a finite volume discretization for a fourth order diffusion equation. Nonlinearity 29 (2016) 1992–2023. [Google Scholar]
  28. A. Mielke, A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems. Nonlinearity 24 (2011) 1329–1346. [Google Scholar]
  29. F. Otto and E. Weinan, Thermodynamically driven incompressible fluid mixtures. J. Chem. Phys. 107 (1997) 10177–10184. [Google Scholar]
  30. D.L. Scharfetter and H.K. Gummel, Large-signal analysis of a silicon read diode oscillator. IEEE Trans. Electron Dev. 16 (1969) 64–77. [Google Scholar]
  31. C. Villani, Optimal transport. In: Vol. 338 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (2009). Old and new. [Google Scholar]
  32. W. E and P. Palffy-Muhoray, Phase separation in incompressible systems. Phys. Rev. E 55 (1997) R3844–R3846. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you