A priori and a posteriori estimates for three-dimensional Stokes equations with nonstandard boundary conditions, Numerical Methods for Partial Differential Equations, vol.9, issue.4, pp.1178-1193, 2012. ,
DOI : 10.1002/num.20676
Vector potentials in three-dimensional non-smooth domains, Mathematical Methods in the Applied Sciences, vol.2, issue.9, pp.823-864, 1998. ,
DOI : 10.1002/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO;2-B
On 3D DDFV discretization of gradient and divergence operators. I. Meshing, operators and discrete duality, IMA Journal of Numerical Analysis, vol.32, issue.4, pp.1574-1603, 2012. ,
DOI : 10.1093/imanum/drr046
URL : https://hal.archives-ouvertes.fr/hal-00355212
Finite element exterior calculus: from Hodge theory to numerical stability, Bulletin of the American Mathematical Society, vol.47, issue.2, pp.281-354, 2010. ,
DOI : 10.1090/S0273-0979-10-01278-4
Mimetic finite difference method for the Stokes problem on polygonal meshes, Journal of Computational Physics, vol.228, issue.19, pp.7215-7232, 2009. ,
DOI : 10.1016/j.jcp.2009.06.034
Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes, SIAM Journal on Numerical Analysis, vol.48, issue.4, pp.1419-1443, 2010. ,
DOI : 10.1137/090757411
A mimetic discretization of the Stokes problem with selected edge bubbles, SIAM J. Sci. Comput, vol.32, issue.2, pp.875-893, 2010. ,
Spectral Discretization of the Vorticity, Velocity, and Pressure Formulation of the Stokes Problem, SIAM Journal on Numerical Analysis, vol.44, issue.2, pp.826-850, 2006. ,
DOI : 10.1137/050622687
URL : https://hal.archives-ouvertes.fr/hal-00112164
Principles of mimetic discretizations of differential operators of The IMA Volumes in mathematics and its applications, Compatible Spatial Discretization, pp.89-120, 2005. ,
Compatible Discrete Operator Schemes for Elliptic and Stokes Equations on Polyhedral Meshes, 2014. ,
URL : https://hal.archives-ouvertes.fr/tel-01116527
Analysis of Compatible Discrete Operator schemes for elliptic problems on polyhedral meshes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.2, pp.553-581, 2014. ,
DOI : 10.1051/m2an/2013104
URL : https://hal.archives-ouvertes.fr/hal-00751284
Computational electromagnetism and geometry, J. Japan Soc. Appl. Electromagn. & Mech, vol.102, issue.1 2 39 4 5 6, pp.7-8150, 1999. ,
On variational formulations for the Stokes equations with nonstandard boundary conditions, ESAIM: Mathematical Modelling and Numerical Analysis, vol.28, issue.7, pp.903-919, 1994. ,
DOI : 10.1051/m2an/1994280709031
Mimetic finite differences for elliptic problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.43, issue.2, pp.277-295, 2009. ,
DOI : 10.1051/m2an:2008046
Mixed and Hydbrid Finite Element Methods. Springer series in computational mathematics, 1991. ,
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM Journal on Numerical Analysis, vol.43, issue.5, pp.1872-1896, 2005. ,
DOI : 10.1137/040613950
A CONSTRUCTION OF SPACES OF COMPATIBLE DIFFERENTIAL FORMS ON CELLULAR COMPLEXES, Mathematical Models and Methods in Applied Sciences, vol.18, issue.05, pp.739-757, 2008. ,
DOI : 10.1142/S021820250800284X
Discrete Electromagnetism with the Finite Integration Technique, Progress In Electromagnetics Research, vol.32, pp.65-87, 2001. ,
DOI : 10.2528/PIER00080103
A new set of basis functions for the discrete geometric approach, Journal of Computational Physics, vol.229, issue.19, pp.7401-7410, 2010. ,
DOI : 10.1016/j.jcp.2010.06.023
Convergence of electromagnetic problems modelled by Discrete Geometric Approach, CMES, vol.58, issue.1, pp.15-44, 2010. ,
A Discrete Duality Finite Volume discretization of the vorticityvelocity-pressure formulation of the 2D Stokes problem on almost arbitrary two-dimensional grids, 2013. ,
Discrete Exterior Calculus, p.508341, 2005. ,
An extension of the Crouzeix???Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow, Mathematics of Computation, vol.84, issue.291, 2014. ,
DOI : 10.1090/S0025-5718-2014-02861-5
URL : https://hal.archives-ouvertes.fr/hal-00753660
Study of the mixed finite volume method for Stokes and Navier-Stokes equations, Numerical Methods for Partial Differential Equations, vol.7, issue.1, pp.137-171, 2009. ,
DOI : 10.1002/num.20333
URL : https://hal.archives-ouvertes.fr/hal-00110911
Une formulation tourbillon-vitesse-presion pour le problème de Stokes, Comptes Rendus de l'Académie des Sciences, pp.277-280, 1992. ,
Vorticity-velocity-pressure formulation for the Stokes problem, Mathematical Methods in the Applied Sciences, vol.12, issue.13, pp.1091-1119, 2002. ,
DOI : 10.1002/mma.328
On MAC schemes on triangular delaunay meshes, their convergence and application to coupled flow problems, Numerical Methods for Partial Differential Equations, vol.48, issue.4, pp.1397-1424, 2014. ,
DOI : 10.1002/num.21875
3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids, Finite Volumes for Complex Applications VI -Problems & Perspectives, pp.95-130, 2011. ,
DOI : 10.1007/978-3-642-20671-9_89
URL : https://hal.archives-ouvertes.fr/hal-00580549
Stokes Complexes and the Construction of Stable Finite Elements with Pointwise Mass Conservation, SIAM Journal on Numerical Analysis, vol.51, issue.2, pp.1308-1326, 2013. ,
DOI : 10.1137/120888132
An Introduction to a Compatible Spectral Discretization Method, Mechanics of Advanced Materials and Structures, vol.35, issue.3, pp.48-67, 2012. ,
DOI : 10.1006/jcph.2001.6973
Discrete Hodge-Operators: An Algebraic Perspective, Progress In Electromagnetics Research, vol.32, pp.247-269, 2001. ,
DOI : 10.2528/PIER00080110
Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution, Journal of Computational Physics, vol.240, pp.284-309, 2013. ,
DOI : 10.1016/j.jcp.2012.10.043
The Discrete Duality Finite Volume Method for Stokes Equations on Three-Dimensional Polyhedral Meshes, SIAM Journal on Numerical Analysis, vol.50, issue.2, 2012. ,
DOI : 10.1137/110831593
On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime, Computer Methods in Applied Mechanics and Engineering, vol.268, pp.782-800, 2014. ,
DOI : 10.1016/j.cma.2013.10.011
The finite volume, finite element, and finite difference methods as numerical methods for physical field problems Advances in Imaging and electron physics, pp.1-146, 2000. ,
Finite Element Methods for Maxwell's Equations. Numerical Mathematics and Scientific Computation, 2003. ,
Incompressible mixed finite elements for Stokes equations, Numerische Mathematik, vol.12, issue.1, pp.97-112, 1982. ,
DOI : 10.1007/BF01399314
Discrete Conservation Properties of Unstructured Mesh Schemes, Annual Review of Fluid Mechanics, vol.43, issue.1, pp.299-318, 2011. ,
DOI : 10.1146/annurev-fluid-122109-160645
A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows, Journal of Computational Physics, vol.184, issue.1, pp.192-214, 2003. ,
DOI : 10.1016/S0021-9991(02)00027-X
Discrete calculus methods for diffusion, Journal of Computational Physics, vol.224, issue.1, pp.59-81, 2007. ,
DOI : 10.1016/j.jcp.2006.12.022
Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques [for EM field analysis], IEEE Transactions on Magnetics, vol.35, issue.3, pp.1494-1497, 1999. ,
DOI : 10.1109/20.767250
Differential Forms in Lattice Field Theories: An Overview, ISRN Mathematical Physics, vol.33, issue.15, p.16, 2013. ,
DOI : 10.1063/1.3692167
On the formal structure of physical theories. Istituto di matematica, 1975. ,
Finite formulation of the electromagnetic field, Progress In Electromagnetics Research (PIER), pp.1-44, 2001. ,
High order finite element methods for electromagnetic field computation, 2006. ,