A new mimetic finite difference method for the diffusion problem is developed by using a linear interpolation for the numerical fluxes. This approach provides a higher-order accurate approximation to the flux of the exact solution. In analogy with the original formulation, a family of local scalar products is constructed to satisfy the fundamental properties of local consistency and spectral stability. The scalar solution field is approximated by a piecewise constant function. A computationally efficient postprocessing technique is also proposed to get a piecewise quadratic polynomial approximation to the exact scalar variable. Finally, optimal convergence rates and accuracy improvement with respect to the lower-order formulation are shown by numerical examples. © 2008 Society for Industrial and Applied Mathematics.

BEIRAO DA VEIGA, L., Manzini, G. (2008). The higher-order formulation of the mimetic finite difference method. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 31(1), 732-760 [10.1137/080717894].

### The higher-order formulation of the mimetic finite difference method

#### Abstract

A new mimetic finite difference method for the diffusion problem is developed by using a linear interpolation for the numerical fluxes. This approach provides a higher-order accurate approximation to the flux of the exact solution. In analogy with the original formulation, a family of local scalar products is constructed to satisfy the fundamental properties of local consistency and spectral stability. The scalar solution field is approximated by a piecewise constant function. A computationally efficient postprocessing technique is also proposed to get a piecewise quadratic polynomial approximation to the exact scalar variable. Finally, optimal convergence rates and accuracy improvement with respect to the lower-order formulation are shown by numerical examples. © 2008 Society for Industrial and Applied Mathematics.
##### Scheda breve Scheda completa Scheda completa (DC)
Articolo in rivista - Articolo scientifico
Boundary value problem; Diffusion equation; High-order scheme; Mimetic finite difference method; Postprocessing; Unstructured polyhedral mesh
English
2008
31
1
732
760
none
BEIRAO DA VEIGA, L., Manzini, G. (2008). The higher-order formulation of the mimetic finite difference method. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 31(1), 732-760 [10.1137/080717894].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/99191`
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