A cell-centred finite volume approximation for second order partial derivative operators with full matrix on unstructured meshes in any space dimension
Numerical Analysis
2016-08-16 v1
Abstract
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 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.
Cite
@article{arxiv.math/0505109,
title = {A cell-centred finite volume approximation for second order partial derivative operators with full matrix on unstructured meshes in any space dimension},
author = {Robert Eymard and Thierry Gallouët and Raphaèle Herbin},
journal= {arXiv preprint arXiv:math/0505109},
year = {2016}
}