A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes

By Francois Hermeline. 2000

252 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/90cc4e42bcf9e23f9acac5b217c669b31968c59e

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A monotone nonlinear finite volume method for approximating diffusion operators on general meshes (2016, methodology): “Note that these two independent linear systems are also those that would be gotten with the DDFV method; see [14] and [15].”
Finite Volume Methods: Foundation and Analysis (2004, methodology): “The second approach, which is widely used in the numerical analysis of conservation laws, is based on the doubling of variables technique of Kruzkov; see Kruzkov (1970) and Kuznetsov (1976). In essence, this technique enables one to estimate the error between the exact and approximate solution of a ”
Mimetic finite difference method (2014, methodology): “Instead, an exact duality relation is satisfied by the discrete duality finite volume (DDFV) method for two-dimensional diffusion problems in [95,136,137].”
Stabilized DDFV schemes for stokes problem with variable viscosity on general 2D meshes (2011, methodology): “Stabilized DDFV Schemes for Stokes Problem with Variable Viscosity on General 2D Meshes Stella Krell Laboratoire d’Analyse, Topologie et Probabilités, Université de Provence,”
A FINITE VOLUME METHOD FOR THE LAPLACE EQUATION ON ALMOST ARBITRARY TWO-DIMENSIONAL GRIDS (2005, methodology): “More general anisotropic and/or non-linear diffusion operators were studied numerically in [15]; the setting of these problems into the formalism of discrete operators on general grids, as well as the coupling with convection terms is the subject of current investigations.”
Discrete duality finite volume schemes for Leray−Lions−type elliptic problems on general 2D meshes (2007, methodology): “We consider the discrete gradient introduced by Coudi(cid:18)ere and al. in [8] and applied by Hermeline [22] and Domelevo and Omn(cid:18)es [11] in the framework of DDFV schemes described above.”