Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes SUSHI: a scheme using stabilisation and hybrid interfaces
نویسنده
چکیده
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 accurate on several numerical examples. Mathematical convergence of the approximate solution to the continuous solution is obtained for general (possibly discontinuous) tensors, general (possibly non-conforming) meshes, and with no regularity assumption on the solution. An error estimate is then drawn under sufficient regularity assumptions on the solution.
منابع مشابه
Discretisation of heterogeneous and anisotropic diffusion problems
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 sh...
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Abstract: A discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes is developed and studied. The unknowns of this scheme are the values at the center of the control volumes and at some internal interfaces, chosen because of some irregularity of the diffusion tensor. If the tensor is regular enough, the values on the interfaces may be deduced from the ...
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Abstract: A discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes is developed and studied. The unknowns of this scheme are the values at the center of the control volumes and at some internal interfaces, chosen because of some irregularity of the diffusion tensor. If the tensor is regular enough, the values on the interfaces may be deduced from the ...
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A discretization of heterogeneous and anisotropic diffusion problems on general discretization meshes is developed and studied. The unknowns of this scheme are the values at the center of the control volumes and at some internal interfaces, chosen because of some irregularity of the diffusion tensor. If the tensor is regular enough, the values on the interfaces may be deduced from the values at...
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