A. Arnold, P. Markowich, G. Toscani, and A. Unterreiter, On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations, Comm. Partial Differential Equations, vol.26, pp.43-100, 2001.

R. Bailo, J. A. Carrillo, and J. Hu, Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient flow structure, 2018.

M. Bessemoulin-chatard and C. Chainais-hillairet, Exponential decay of a finite volume scheme to the thermal equilibrium for drift-diffusion systems, J. Numer. Math, vol.25, pp.147-168, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01250709

M. Bessemoulin-chatard, C. Chainais-hillairet, and F. Filbet, On discrete functional inequalities for some finite volume schemes, IMA J. Numer. Anal, vol.35, pp.1125-1149, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00672591

M. Bessemoulin-chatard, M. Herda, and T. Rey, Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations, Math. Comp, vol.89, pp.1093-1133, 2020.
URL : https://hal.archives-ouvertes.fr/hal-01957832

M. Bessemoulin-chatard and A. , A finite volume scheme for a Keller-Segel model with additional cross-diffusion, IMA J. Numer. Anal, vol.34, pp.96-122, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01116450

R. Bianchini and L. Gosse, A truly two-dimensional discretization of drift-diffusion equations on Cartesian grids, SIAM J. Numer. Anal, vol.56, pp.2845-2870, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02012706

T. Bodineau, J. Lebowitz, C. Mouhot, and C. Villani, Lyapunov functionals for boundary-driven nonlinear driftdiffusion equations, Nonlinearity, vol.27, pp.2111-2132, 2014.

C. Buet and S. Dellacherie, On the Chang and Cooper scheme applied to a linear Fokker-Planck equation, Commun. Math. Sci, vol.8, pp.1079-1090, 2010.

C. Cancès, C. Chainais-hillairet, and S. Krell, Numerical analysis of a nonlinear free-energy diminishing discrete duality finite volume scheme for convection diffusion equations, Comput. Methods Appl. Math, vol.18, pp.407-432, 2018.

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, vol.17, pp.1525-1584, 2017.

J. A. Carrillo, A. Jüngel, P. A. Markowich, G. Toscani, and A. Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Monatsh. Math, vol.133, pp.1-82, 2001.

J. A. Carrillo and G. Toscani, Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations, Math. Methods Appl. Sci, vol.21, pp.1099-1476, 1998.

C. Chainais-hillairet and M. Herda, Large-time behaviour of a family of finite volume schemes for boundary-driven convection-diffusion equations, IMA Journal of Numerical Analysis, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01885015

C. Chainais-hillairet, A. Jüngel, and S. Schuchnigg, Entropy-dissipative discretization of nonlinear diffusion equations and discrete Beckner inequalities, ESAIM Math. Model. Numer. Anal, vol.50, pp.135-162, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00924282

J. Chang and G. Cooper, A practical difference scheme for fokker-planck equations, Journal of Computational Physics, vol.6, pp.1-16, 1970.

Y. Coudière, J. Vila, and P. Villedieu, Convergence rate of a finite volume scheme for a two-dimensional convection-diffusion problem, M2AN Math. Model. Numer. Anal, vol.33, pp.493-516, 1999.

K. Deimling, Nonlinear functional analysis, 1985.

L. Desvillettes and K. Fellner, Entropy methods for reaction-diffusion equations with degenerate diffusion arising in reversible chemistry, 2007.

K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, M2AN Math. Model. Numer. Anal, vol.39, pp.1203-1249, 2005.

J. Droniou, Finite volume schemes for diffusion equations: introduction to and review of modern methods, Math. Models Methods Appl. Sci, vol.24, pp.1575-1619, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00813613

J. Droniou, R. Eymard, T. Gallouët, C. Guichard, and R. Herbin, The gradient discretisation method, vol.82, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01382358

G. Dujardin, F. Hérau, and P. Lafitte, Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker-Planck equations, Numer. Math, vol.144, pp.615-697, 2020.
URL : https://hal.archives-ouvertes.fr/hal-01702545

R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods, Handbook of numerical analysis, vol.VII, pp.713-1020, 2000.
URL : https://hal.archives-ouvertes.fr/hal-02100732

F. Filbet and M. Herda, A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure, Numer. Math, vol.137, pp.535-577, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01326029

L. Gosse, Aliasing and two-dimensional well-balanced for drift-diffusion equations on square grids, Math. Comp, vol.89, pp.139-168, 2020.

R. Herbin and F. Hubert, Benchmark on discretization schemes for anisotropic diffusion problems on general grids, Finite Volumes for Complex, pp.659-692, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00580549

A. , Il'in, A difference scheme for a differential equation with a small parameter multiplying the highest derivative, Mat. Zametki, vol.6, pp.237-248, 1969.

E. W. Larsen, C. D. Levermore, G. C. Pomraning, and J. G. Sanderson, Discretization methods for onedimensional Fokker-Planck operators, J. Comput. Phys, vol.61, issue.85, pp.90070-90071, 1985.

J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. École Norm. Sup, issue.3, pp.45-78, 1934.

L. Li and J. Liu, Large time behaviors of upwind schemes and B-schemes for Fokker-Planck equations on R by jump processes, 2020.

H. Liu and H. Yu, An entropy satisfying conservative method for the Fokker-Planck equation of the finitely extensible nonlinear elastic dumbbell model, SIAM J. Numer. Anal, vol.50, pp.1207-1239, 2012.

L. Pareschi and M. Zanella, Structure preserving schemes for nonlinear fokker-planck equations and applications, Journal of Scientific Computing, vol.74, pp.1575-1600, 2018.

D. L. Scharfetter and H. K. Gummel, Large-signal analysis of a silicon read diode oscillator, IEEE Transactions on electron devices, vol.16, pp.64-77, 1969.

G. Toscani, Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation, Quart. Appl. Math, vol.57, pp.521-541, 1999.