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.
|Titolo:||The higher-order formulation of the mimetic finite difference method|
BEIRAO DA VEIGA, LOURENCO (Primo)
|Parole Chiave:||Boundary value problem; Diffusion equation; High-order scheme; Mimetic finite difference method; Postprocessing; Unstructured polyhedral mesh|
|Settore Scientifico Disciplinare:||Settore MAT/08 - Analisi Numerica|
|Data di pubblicazione:||2008|
|Digital Object Identifier (DOI):||10.1137/080717894|
|Appare nelle tipologie:||01 - Articolo su periodico|