Finite element exterior calculus, homological techniques, and applications, Acta Numerica, vol.15, pp.1-155, 2006. ,
Finite element exterior calculus: from Hodge theory to numerical stability, Bull. Amer. Math. Soc. (N.S.), vol.47, pp.281-354, 2010. ,
A new hierarchically-structured n-dimensional covariant form of rotating equations of geophysical fluid dynamics, GEM-International Journal on Geomathematics, vol.7, issue.1, pp.31-101, 2016. ,
A structure-preserving split finite element discretization of the split wave equations, Applied Mathematics and Computation, vol.325, pp.375-400, 2018. ,
, Towards a variational discretization of compressible fluids: the rotating shallow water equations, vol.6, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01958134
Energy-enstrophy conserving compatible finite element schemes for the shallow water equations on rotating domains with boundaries, Journal of Computational Physics, vol.373, pp.171-187, 2018. ,
, Variational integrators for anelastic and pseudoincompressible flows, 2017.
, Towards a variational discretization of compressible fluids: the rotating shallow water equations, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01958134
Mimetic finite difference methods for Hamiltonian wave equations in 2D, Comput. Math. Appl, vol.74, issue.5, pp.1123-1141, 2017. ,
, Principles of mimetic discretizations of differential operators, Compatible Spatial Discretizations, The IMA Volumes in Mathematics and its Applications, vol.142, pp.89-119, 2006.
Mixed finite element methods and applications, Springer series in computational mathematics, 2013. ,
Statistical properties of an enstrophy conserving discretisation for the stochastic quasi-geostrophic equation, Geophysical & Astrophysical Fluid Dynamics, 2018. ,
Generalized finite differences" in computational electromagnetics, Progress In Electromagnetics Research (PIER), vol.32, pp.45-64, 2001. ,
, A Mathematical Theory of Large-scale Atmosphere/ocean Flow, 2006.
Compatible finite elements for numerical weather prediction, Q. J. R. Meteorol. Soc, vol.140, pp.2223-2234, 2014. ,
, Statistical mechanics of Arakawa's discretizations, vol.227, pp.1286-1305, 2007.
, Dispersion analysis of compatible Galerkin schemes on quadrilaterals for shallow water models, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01916382
Variational and Hamiltonian Formulations of Geophysical Fluids using Split Exterior Calculus, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01895935
A finite element exterior calculus framework for the rotating shallow-water equations, Journal of Computational Physics, vol.257, issue.B, pp.1506-1526, 2012. ,
, Discrete exterior calculus, 2005.
Variational discretization for rotating stratified fluids, Discrete Continuous Dynamical Systems-Series A, vol.34, pp.479-511, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01088890
, Geometric, variational discretization of continuum theories, vol.240, pp.1724-1760, 2011.
Mimetic spectral element method for generalized convection-diffusion problems, Proceedings of the European Conference on Computational Fluid Dynamics (ECCOMAS CFD), 2010. ,
, Local coderivatives and approximation of Hodge Laplace problems, 2016.
Physicscompatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms, Journal of Computational Physics, vol.257, issue.B, pp.1394-1422, 2014. ,
Geophysical fluid dynamics, 1979. ,
Analysis of a mixed finite-element pair proposed for an atmospheric dynamical core, Quarterly Journal of the Royal Meteorological Society, vol.139, issue.674, pp.1239-1254, 2013. ,