A unified approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume methodsReportar como inadecuado




A unified approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume methods - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier 2 LETEM - Laboratoire d-Etudes des Transferts d-Energie et de Matière 3 LATP - Laboratoire d-Analyse, Topologie, Probabilités

Abstract : We investigate the connections between several recent methods for the discretization of ani\-so\-tropic 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 method 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, obtaining as a by-product an explicit lifting operator close to the ones used in some theoretical studies of the Mimetic Finite Difference scheme. 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.





Autor: Jerome Droniou - Robert Eymard - Thierry Gallouët - Raphaele Herbin -

Fuente: https://hal.archives-ouvertes.fr/



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