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

  • Authors:
  • Jérôme Droniou;Robert Eymard

  • Affiliations:
  • Département de Mathématiques, UMR CNRS 5149, CC 051, Université Montpellier II, Place Eugène Bataillon, 34095, Montpellier cedex 5, France;Laboratoire d’Analyse et de Mathématiques Appliquées, UMR 8050, Université de Marne-la-Vallée, 5 boulevard Descartes, Champs-sur-Marne, 77454, Marne-la-Vall� ...

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2006

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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.