A mixed finite volume scheme for anisotropic diffusion problems on any grid

Jérôme Droniou, Robert Eymard

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Abstract

We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. The approximate solution is shown to converge to the continuous one as the size of the mesh tends to 0, and an error estimate is given. An easy implementation method is then proposed, and the efficiency of the scheme is shown on various types of grids and for various diffusion matrices.

Original languageEnglish
Pages (from-to)35-71
Number of pages37
JournalNumerische Mathematik
Volume105
Issue number1
DOIs
Publication statusPublished - 1 Nov 2006
Externally publishedYes

Keywords

  • Anisotropic heterogeneous diffusion problems
  • Finite volume scheme
  • Irregular grids
  • Unstructured grids

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