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Article Dans Une Revue Mathematics of Computation Année : 2012

Finite volume schemes for the biharmonic problem on general meshes

Résumé

Finite volume schemes for the approximation of a biharmonic problem with Dirichlet boundary conditions are constructed and analyzed, first on grids which satisfy an orthogonality condition, and then on general, possibly non conforming meshes. In both cases, the piece-wise constant approximate solution is shown to converge in L2 () to the exact solution; similar results are shown for the discrete approximate of the gradient and the discrete approximate of the Laplacian of the exact solution. Error estimates are also derived. These results are confirmed by numerical results.
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Dates et versions

hal-00475419 , version 1 (21-04-2010)
hal-00475419 , version 2 (25-08-2011)

Identifiants

  • HAL Id : hal-00475419 , version 2

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Robert Eymard, Thierry Gallouët, Raphaele Herbin, Alexander Linke. Finite volume schemes for the biharmonic problem on general meshes. Mathematics of Computation, 2012, 81 (280), pp.2019-2048. ⟨hal-00475419v2⟩
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