Chapter

Benchmark 3D: the VAG scheme

DOI: 10.1007/978-3-642-20671-9_99

ABSTRACT Let Ωbe a bounded open domain of

\mathbbR3\mathbb{R}^3
let
feL2(W)f\epsilon\rm L^2(\Omega)
and let
L\Lambda
be a measurable function from Ω to the set

m3(\mathbbR) of 3 3m^3(\mathbb{R)} of 3 \times 3
matrices, such that for a.e.

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    ABSTRACT: We present here a number of test cases and meshes which were designed to form a benchmark for finite volume schemes and give a summary of some of the results which were presented by the participants to this benchmark. We address a two-dimensional anisotropic diffusion problem, which is discretized on general, possibly non-conforming meshes. In most cases, the diffusion tensor is taken to be anisotropic, and at times heterogeneous and/or dis-continuous. The meshes are either triangular or quadrangular, and sometimes quite distorted. Several methods were tested, among which finite element, discontinous Galerkin, cell centred and vertex centred finite volume methods, discrete duality finite volume methods, mimetic meth-ods. The results given by the participants to the benchmark range from the number of unknowns, the errors on the fluxes or the minimum and maximum values and energy, to the order of con-vergence (when available).
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