Cell - Centered Scheme For Heterogeneous

We present a new scheme for the discretization of heterogeneous anisotropic di usion problems on general meshes. With light assumptions, we show that the algorithm can be written as a cell-centered scheme with a small stencil and that it is convergent for discontinuous tensors. The key point of the proof consists in showing both the strong and the weak consistency of the method. Besides, we study non-linear corrections to correct the FECC scheme, in order to satisfy the discrete maximum principle (DMP). The e ciency of the scheme is demonstrated through numerical tests of the 5th & 6th International Symposium on Finite Volumes for Complex Applications FVCA 5 & 6. Moreover, the comparison with classical nite volume schemes emphasizes the precision of the method. We also show the good behaviour of the algorithm for nonconforming meshes. In addition, we give some numerical tests to check the existence for the non-linear FECC schemes.