]. C. Cotter and J. Shipton, Mixed finite elements for numerical weather prediction, Journal of Computational Physics, vol.231, issue.21
DOI : 10.1016/j.jcp.2012.05.020

URL : http://arxiv.org/pdf/1103.2440

A. Natale, J. Shipton, and C. J. Cotter, Compatible finite element spaces for geophysical fluid dynamics, Dynamics and Statistics of the Climate System, vol.140, issue.1
DOI : 10.1002/qj.2235

URL : https://academic.oup.com/climatesystem/article-pdf/1/1/dzw005/13106953/dzw005.pdf

R. Hiemstra, D. Toshniwal, R. Huijsmans, and M. Gerritsma, High order geometric methods with exact conservation properties, Journal of Computational Physics, vol.257, pp.1444-1471, 2014.
DOI : 10.1016/j.jcp.2013.09.027

D. N. Arnold, R. S. Falk, and R. Winther, Finite element exterior calculus, homological techniques, and applications, Acta Numerica, vol.15, 2006.
DOI : 10.1017/S0962492906210018

URL : http://www.ifi.uio.no/~rwinther/acta.pdf

V. Rostand, D. Y. Roux, and G. Carey, Kernel Analysis of the Discretized Finite Difference and Finite Element Shallow-Water Models, SIAM Journal on Scientific Computing, vol.31, issue.1, pp.531-556, 2008.
DOI : 10.1137/070695198

V. Rostand and D. Y. Le-roux, Raviart???Thomas and Brezzi???Douglas???Marini finite???element approximations of the shallow???water equations, International Journal for Numerical Methods in Fluids, vol.127, issue.8, pp.951-976, 2008.
DOI : 10.1111/j.1600-0870.1984.tb00235.x

D. Y. Roux, Spurious inertial oscillations in shallow-water models, Journal of Computational Physics, vol.231, issue.24
URL : https://hal.archives-ouvertes.fr/hal-00864893

A. Arakawa and V. R. Lamb, Computational design of the basic dynamical processes of the ucla general circulation model 17 (Supplement C) (1977) 173 ? 265. doi:https://doi

D. Y. Roux, V. Rostand, and B. Pouliot, Analysis of Numerically Induced Oscillations in 2D Finite???Element Shallow???Water Models Part I: Inertia???Gravity Waves, SIAM Journal on Scientific Computing, vol.29, issue.1, pp.331-360, 2007.
DOI : 10.1137/060650106

D. Y. Roux and B. Pouliot, Analysis of Numerically Induced Oscillations in Two-Dimensional Finite-Element Shallow-Water Models Part II: Free Planetary Waves, SIAM Journal on Scientific Computing, vol.30, issue.4, pp.1971-1991, 2008.
DOI : 10.1137/070697872

T. Melvin, A. Staniforth, and J. Thuburn, Dispersion analysis of the spectral element method, Quarterly Journal of the Royal Meteorological Society, vol.135, issue.668, 1906.
DOI : 10.1175/2007MWR2058.1

URL : http://onlinelibrary.wiley.com/doi/10.1002/qj.1906/pdf

M. Ainsworth and H. A. Wajid, Dispersive and Dissipative Behavior of the Spectral Element Method, SIAM Journal on Numerical Analysis, vol.47, issue.5, pp.3910-3937, 2009.
DOI : 10.1137/080724976

M. Ainsworth, Dispersive behaviour of high order finite element schemes for the one-way wave equation, Journal of Computational Physics, vol.259
DOI : 10.1016/j.jcp.2013.11.003

URL : http://www.newton.ac.uk/preprints/NI13003.pdf

J. Thuburn and C. J. Cotter, A primal???dual mimetic finite element scheme for the rotating shallow water equations on polygonal spherical meshes, Journal of Computational Physics, vol.290, pp.274-297, 2015.
DOI : 10.1016/j.jcp.2015.02.045

URL : http://arxiv.org/pdf/1409.8130

T. Melvin and J. Thuburn, Wave dispersion properties of compound finite elements, Journal of Computational Physics, vol.338, issue.261, pp.68-90, 2009.
DOI : 10.1016/j.jcp.2017.02.025

URL : https://doi.org/10.1016/j.jcp.2017.02.025

A. Staniforth, T. Melvin, and C. Cotter, Analysis of a mixed finite-element pair proposed for an atmospheric dynamical core, Quarterly Journal of the Royal Meteorological Society, vol.138, issue.674, pp.1239-1254, 2013.
DOI : 10.1002/qj.958

URL : http://onlinelibrary.wiley.com/doi/10.1002/qj.2028/pdf

T. Melvin, A. Staniforth, and C. Cotter, A two-dimensional mixed finite-element pair on rectangles, Quarterly Journal of the Royal Meteorological Society, vol.138, issue.680, pp.930-942, 2014.
DOI : 10.1002/qj.958

T. Melvin, mixed finite element pair for atmospheric modelling, Journal of Computational Physics, vol.355, pp.342-365, 2018.
DOI : 10.1016/j.jcp.2017.11.019

P. D. Powell, Calculating Determinants of Block Matrice- sarXiv:1112, p.4379

J. Banks and T. Hagstrom, On Galerkin difference methods, Journal of Computational Physics, vol.313, pp.310-327, 2016.
DOI : 10.1016/j.jcp.2016.02.042

URL : https://manuscript.elsevier.com/S0021999116001121/pdf/S0021999116001121.pdf

E. Kritsikis and T. Dubos, Higher-order finite elements for the shallow-water equations on the cubed sphere, PDEs on the Sphere Workshop, 2014.

A. Buffa, J. Rivas, G. Sangalli, and R. Vazquez, Isogeometric Discrete Differential Forms in Three Dimensions, SIAM Journal on Numerical Analysis, vol.49, issue.2, pp.818-844, 2011.
DOI : 10.1137/100786708

A. Buffa, G. Sangalli, and R. Vazquez, Isogeometric methods for computational electromagnetics: B-spline and t-spline discretizations2014) 1291 ? 1320, physics-compatible numerical methods. doi:https, Journal of Computational PhysicsPart B), vol.257
DOI : 10.1016/j.jcp.2013.08.015

URL : http://arxiv.org/pdf/1209.2048

A. Sarmiento, A. Cortes, D. Garcia, L. Dalcin, N. Collier et al., PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces, Journal of Computational Science, vol.18
DOI : 10.1016/j.jocs.2016.09.010

URL : http://arxiv.org/pdf/1602.08727

J. Kent, J. P. Whitehead, C. Jablonowski, and R. B. Rood, Determining the effective resolution of advection schemes. Part I: Dispersion analysis, Journal of Computational Physics, vol.278, pp.485-496, 2014.
DOI : 10.1016/j.jcp.2014.01.043

J. Kent, C. Jablonowski, J. P. Whitehead, and R. B. Rood, Determining the effective resolution of advection schemes. Part II: Numerical testing, Journal of Computational Physics, vol.278
DOI : 10.1016/j.jcp.2014.08.045

P. A. Ullrich, Understanding the treatment of waves in atmospheric models. Part 1: The shortest resolved waves of the 1D linearized shallow-water equations, Quarterly Journal of the Royal Meteorological Society, vol.195, issue.682
DOI : 10.1016/j.jcp.2003.10.014