# Mimetic finite differences for elliptic problems

Franco Brezzi; Annalisa Buffa; Konstantin Lipnikov

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 43, Issue: 2, page 277-295
- ISSN: 0764-583X

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topBrezzi, Franco, Buffa, Annalisa, and Lipnikov, Konstantin. "Mimetic finite differences for elliptic problems." ESAIM: Mathematical Modelling and Numerical Analysis 43.2 (2008): 277-295. <http://eudml.org/doc/194451>.

@article{Brezzi2008,

abstract = {
We developed a mimetic finite difference method for solving elliptic equations
with tensor coefficients on polyhedral meshes. The first-order convergence
estimates in a mesh-dependent H1 norm are derived.
},

author = {Brezzi, Franco, Buffa, Annalisa, Lipnikov, Konstantin},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Finite differences; polyhedral meshes; diffusion equation; error estimates.; mimetic finite differences; error estimates; convergence; Dirichlet boundary value model problem; numerical comparisons; finite element method},

language = {eng},

month = {12},

number = {2},

pages = {277-295},

publisher = {EDP Sciences},

title = {Mimetic finite differences for elliptic problems},

url = {http://eudml.org/doc/194451},

volume = {43},

year = {2008},

}

TY - JOUR

AU - Brezzi, Franco

AU - Buffa, Annalisa

AU - Lipnikov, Konstantin

TI - Mimetic finite differences for elliptic problems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/12//

PB - EDP Sciences

VL - 43

IS - 2

SP - 277

EP - 295

AB -
We developed a mimetic finite difference method for solving elliptic equations
with tensor coefficients on polyhedral meshes. The first-order convergence
estimates in a mesh-dependent H1 norm are derived.

LA - eng

KW - Finite differences; polyhedral meshes; diffusion equation; error estimates.; mimetic finite differences; error estimates; convergence; Dirichlet boundary value model problem; numerical comparisons; finite element method

UR - http://eudml.org/doc/194451

ER -

## References

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- L. Margolin, M. Shashkov and P. Smolarkiewicz, A discrete operator calculus for finite difference approximations. Comput. Meth. Appl. Mech. Engrg.187 (2000) 365–383.
- P.A. Raviart and J.-M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of the Finite Element Method, I. Galligani and E. Magenes Eds., Springer-Verlag, Berlin-Heilderberg-New York (1977) 292–315.

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- Robert Eymard, Cindy Guichard, Raphaèle Herbin, Small-stencil 3D schemes for diffusive flows in porous media
- Jérôme Bonelle, Alexandre Ern, Analysis of Compatible Discrete Operator schemes for elliptic problems on polyhedral meshes
- Imbunm Kim, Zhongxuan Luo, Zhaoliang Meng, Hyun NAM, Chunjae Park, Dongwoo Sheen, A piecewise P2-nonconforming quadrilateral finite element

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