, 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
, Discrete duality finite volume schemes for Leray???Lions???type elliptic problems on general 2D meshes, Numerical Methods for Partial Differential Equations, vol.152, issue.1, pp.145-195, 2007.
DOI : 10.1002/num.20170
URL : https://hal.archives-ouvertes.fr/hal-00005779
, Finite element exterior calculus, homological techniques, and applications, Acta Numerica, vol.15, pp.1-155, 2006.
DOI : 10.1017/S0962492906210018
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.118.9322
, Principles of mimetic discretizations of differential operators of The IMA Volumes in mathematics and its applications, Compatible Spatial Discretization, pp.89-120, 2005.
, On the geometry of electromagnetism, J. Japan Soc. Appl. Electromagn. & Mech, vol.6, issue.1 2 3 4, pp.17-28, 1998.
, Computational electromagnetism and geometry, J. Japan Soc. Appl. Electromagn. & Mech, vol.102, issue.1 2 39 4 5 6, pp.7-8150, 1999.
, 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
, 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 dual finite element complex on the barycentric refinement, Mathematics of Computation, vol.76, issue.260, pp.1743-1769, 2007.
DOI : 10.1090/S0025-5718-07-01965-5
, 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
, Topics in structure-preserving discretization, Acta Numerica, vol.29, pp.1-119, 2011.
DOI : 10.1002/(SICI)1521-4001(199812)78:12<795::AID-ZAMM795>3.0.CO;2-P
, Base functions and discrete constitutive relations for staggered polyhedral grids, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.9-12, pp.9-121117, 2009.
DOI : 10.1016/j.cma.2008.11.021
, 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.
, Discrete Exterior Calculus, 2005.
, Mathematical Aspects of Discontinuous Galerkin Methods, of SMAI Mathmatiques et Applications, 2012.
DOI : 10.1007/978-3-642-22980-0
, Finite-Difference Approach to the Hodge Theory of Harmonic Forms, American Journal of Mathematics, vol.98, issue.1, pp.79-104, 1976.
DOI : 10.2307/2373615
, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.6, pp.1203-1249, 2005.
DOI : 10.1051/m2an:2005047
, A mixed finite volume scheme for anisotropic diffusion problems on any grid, Numerische Mathematik, vol.59, issue.1, pp.35-71, 2006.
DOI : 10.1007/s00211-006-0034-1
URL : https://hal.archives-ouvertes.fr/hal-00005565
, A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS, Mathematical Models and Methods in Applied Sciences, vol.20, issue.02, pp.265-295, 2010.
DOI : 10.1142/S0218202510004222
URL : https://hal.archives-ouvertes.fr/hal-00346077
, Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces, IMA Journal of Numerical Analysis, vol.30, issue.4, pp.1009-1043, 2010.
DOI : 10.1093/imanum/drn084
, Small-stencil 3D schemes for diffusive flows in porous media, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.2, pp.265-290, 2012.
DOI : 10.1051/m2an/2011040
URL : https://hal.archives-ouvertes.fr/hal-00542667
, 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
, Stability of dual discretization methods for partial differential equations, 2011.
, Discrete Hodge-Operators: An Algebraic Perspective, Progress In Electromagnetics Research, vol.32, pp.247-269, 2001.
DOI : 10.2528/PIER00080110
, Covolume techniques for anisotropic media, Numerische Mathematik, vol.24, issue.1, pp.215-234, 1992.
DOI : 10.1007/BF01385505
, Deriving mimetic difference approximations to differential operators using algebraic topology, 1988.
, Mimetic framework on curvilinear quadrilaterals of arbitrary order, 2011.
, The finite volume, finite element, and finite difference methods as numerical methods for physical field problems, of Advances in Imaging and Electron Physics, pp.1-146, 2000.
DOI : 10.1016/S1076-5670(00)80012-9
, 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
, On the formal structure of physical theories, 1975.
, MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS, Mathematical Models and Methods in Applied Sciences, vol.23, issue.05, pp.803-838, 2013.
DOI : 10.1142/S0218202512500613
, Geometric integration theory, 1957.
DOI : 10.1515/9781400877577
, High order finite element methods for electromagnetic field computation, 2006.