Discretisation of heterogeneous and anisotropic diffusion problems
نویسنده
چکیده
A symmetric discretisation scheme for heterogeneous anisotropic diffusion problems on general meshes is developed and studied. The unknowns of this scheme are the values at the centre of the control volumes and at some internal interfaces which may for instance be chosen at the diffusion tensor discontinuities. The scheme is therefore completely cell-centred if no edge unknown is kept. It is shown to be accurate on several numerical examples. Convergence of the approximate solution to the continuous solution is proved for general (possibly discontinuous) tensors, general (possibly nonconforming) meshes, and with no regularity assumption on the solution. An error estimate is then deduced under suitable regularity assumptions on the solution.
منابع مشابه
Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes SUSHI: a scheme using stabilisation and hybrid interfaces
A discretisation scheme for heterogeneous anisotropic diffusion problems on general meshes is developed and studied. The unknowns of this scheme are the values at the centre of the control volumes and at some internal interfaces which may for instance be chosen at the diffusion tensor discontinuities. The scheme is therefore completely cell centred if no edge unknown is kept. It is shown to be ...
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