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Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid interfaces
Abstract : 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.
Cited literature [31 references]
https://hal.archives-ouvertes.fr/hal-00203269
Contributor : Raphaele Herbin Connect in order to contact the contributor
Submitted on : Tuesday, December 9, 2008 - 9:40:34 AM
Last modification on : Saturday, January 15, 2022 - 4:14:25 AM
Long-term archiving on: : Friday, September 24, 2010 - 12:16:12 PM
Contributor : Raphaele Herbin Connect in order to contact the contributor
Submitted on : Tuesday, December 9, 2008 - 9:40:34 AM
Last modification on : Saturday, January 15, 2022 - 4:14:25 AM
Long-term archiving on: : Friday, September 24, 2010 - 12:16:12 PM
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