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Article Dans Une Revue Journal of Numerical Mathematics Année : 2009

Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral grids

Résumé

This work is devoted to the discretisation of non linear elliptic problems on general polyhedral meshes in several space dimensions. The SUSHI scheme which was recently studied for anisotropic heterogeneous problems is applied in its full barycentric version, thus resulting into a cell centred scheme written under variational form, also known as 'SUCCES'. We prove the existence of the approximate solution and its convergence to the weak solution of the continuous solution as the mesh size tends to 0. Numerical examples are shown for the p-Laplacian.
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Dates et versions

hal-00351867 , version 1 (12-01-2009)

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Robert Eymard, Thierry Gallouët, Raphaele Herbin. Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral grids. Journal of Numerical Mathematics, 2009, 17 (3), pp.173--193. ⟨10.1515/JNUM.2009.010⟩. ⟨hal-00351867⟩
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