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A discretisation scheme for heterogeneous anisotropic diffusion problems ongeneral meshes is developed and studied. The unknowns of this scheme are thevalues at the centre of the control volumes and at some internal interfaceswhich may for instance be chosen at the diffusion tensor discontinuities. Thescheme is therefore completely cell centred if no edge unknown is kept. It isshown to be accurate on several numerical examples. Mathematical convergence ofthe approximate solution to the continuous solution is obtained for general(possibly discontinuous) tensors, general (possibly non-conforming) meshes, andwith no regularity assumption on the solution. An error estimate is then drawnunder sufficient regularity assumptions on the solution.

Discretisation of heterogeneous and anisotropic diffusion problems on  general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid  interfaces