A cell-centred finite volume approximation for second order partial derivative operators with full matrix on unstructured meshes in any space dimension - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2006

A cell-centred finite volume approximation for second order partial derivative operators with full matrix on unstructured meshes in any space dimension

Résumé

Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality condition. This discrete gradient is shown to satisfy a strong convergence property on the interpolation of regular functions, and a weak one on functions bounded for a discrete $H^1$ norm. To highlight the importance of both properties, the convergence of the finite volume scheme on a homogeneous Dirichlet problem with full diffusion matrix is proven, and an error estimate is provided. Numerical tests show the actual accuracy of the method.
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Dates et versions

hal-00004840 , version 1 (06-05-2005)

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Robert Eymard, Thierry Gallouët, Raphaèle Herbin. A cell-centred finite volume approximation for second order partial derivative operators with full matrix on unstructured meshes in any space dimension. IMA Journal of Numerical Analysis, 2006, 26, pp.326-353. ⟨hal-00004840⟩
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