Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 265 - 295 |
| Number of pages | 31 |
| Journal | Mathematical Models and Methods in Applied Sciences |
| Volume | 20 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2010 |
| Externally published | Yes |
Cite this
}
A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods. / Droniou, Jerome; Eymard, Robert; Gallouet, Thierry; Herbin, Raphaele.
In: Mathematical Models and Methods in Applied Sciences, Vol. 20, No. 2, 2010, p. 265 - 295.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods
AU - Droniou, Jerome
AU - Eymard, Robert
AU - Gallouet, Thierry
AU - Herbin, Raphaele
PY - 2010
Y1 - 2010
N2 - We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids. We prove that the Mimetic Finite Difference scheme, the Hybrid Finite Volume scheme and the Mixed Finite Volume scheme are in fact identical up to some slight generalizations. As a consequence, some of the mathematical results obtained for each of the methods (such as convergence properties or error estimates) may be extended to the unified common framework. We then focus on the relationships between this unified method and nonconforming Finite Element schemes or Mixed Finite Element schemes. We also show that for isotropic operators, on particular meshes such as triangular meshes with acute angles, the unified method boils down to the well-known efficient two-point flux Finite Volume scheme.
AB - We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids. We prove that the Mimetic Finite Difference scheme, the Hybrid Finite Volume scheme and the Mixed Finite Volume scheme are in fact identical up to some slight generalizations. As a consequence, some of the mathematical results obtained for each of the methods (such as convergence properties or error estimates) may be extended to the unified common framework. We then focus on the relationships between this unified method and nonconforming Finite Element schemes or Mixed Finite Element schemes. We also show that for isotropic operators, on particular meshes such as triangular meshes with acute angles, the unified method boils down to the well-known efficient two-point flux Finite Volume scheme.
UR - http://www.worldscientific.com/doi/abs/10.1142/S0218202510004222
U2 - 10.1142/S0218202510004222
DO - 10.1142/S0218202510004222
M3 - Article
VL - 20
SP - 265
EP - 295
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 2
ER -