Finite volume schemes for the biharmonic problem on general meshes

Robert Eymard; Thierry Gallouët; Raphaele Herbin; Alexander Linke

hal-00475419, version 1

Finite volume schemes for the biharmonic problem on general meshes

Robert Eymard () ¹, Thierry Gallouët ², Raphaele Herbin () ², Alexander Linke () ³

(2010-04-21)

Abstract: 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.

1: Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA)
Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8050 – Fédération de Recherche Bézout
2: Laboratoire d'Analyse, Topologie, Probabilités (LATP)
CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III
3: Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
Forschungsverbund Berlin e.V. (FVB)

hal-00475419, version 1
http://hal.archives-ouvertes.fr/hal-00475419
oai:hal.archives-ouvertes.fr:hal-00475419
From: Raphaele Herbin <>
Submitted on: Wednesday, 21 April 2010 22:38:44
Updated on: Thursday, 25 August 2011 10:43:20

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