WIAS Preprint No. 1482, (2010)

Convergence of a finite volume scheme for the biharmonic problem



Authors

  • Eymard, Robert
  • Gallouët, Thierry
  • Herbin, Raphaèle
  • Linke, Alexander
    ORCID: 0000-0002-0165-2698

2010 Mathematics Subject Classification

  • 31B30 74S10 76M1276M12

2008 Physics and Astronomy Classification Scheme

  • 46.70.-p 83.10.-y

Keywords

  • biharmonic problem, finite volume scheme, convergence proof

Abstract

We propose a finite volume scheme for the approximation of a biharmonic problem with Dirichlet boundary conditions. We prove that the piece-wise constant approximate solution converges to the exact solution, as well as the discrete approximate of the gradient and the discrete approximate of the Laplacian of the exact solution. These results are confirmed by numerical results.

Appeared in

  • Math. Comp., 81 (2012) pp. 2019--2048.

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