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A new discretization methodology for diffusion problems on generalized polyhedral meshes

✍ Scribed by Franco Brezzi; Konstantin Lipnikov; Mikhail Shashkov; Valeria Simoncini

Book ID
104013364
Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
369 KB
Volume
196
Category
Article
ISSN
0045-7825

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✦ Synopsis

We develop a family of inexpensive discretization schemes for diffusion problems on generalized polyhedral meshes with elements having non-planar faces. The material properties are described by a full tensor. We also prove superconvergence for the scalar (pressure) variable under very general assumptions. The theoretical results are confirmed with numerical experiments. In the practically important case of logically cubic meshes with randomly perturbed nodes, the mixed finite element with the lowest order Raviart-Thomas elements does not converge while the proposed mimetic method has the optimal convergence rate.

πŸ“œ SIMILAR VOLUMES

Discrete duality finite volume schemes f
Discrete duality finite volume schemes for Lerayβˆ’Lionsβˆ’type elliptic problems on general 2D meshes
✍ Boris Andreianov; Franck Boyer; Florence Hubert πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 466 KB

## Abstract Discrete duality finite volume schemes on general meshes, introduced by Hermeline and Domelevo and Omnès for the Laplace equation, are proposed for nonlinear diffusion problems in 2D with nonhomogeneous Dirichlet boundary condition. This approach allows the discretization of non linear