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IMA Journal of Numerical Analysis Advance Access published online on June 30, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drp001
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Nonoverlapping Schwarz algorithm for solving two-dimensional m-DDFV schemes

Franck Boyer{dagger}

Université Paul Cézanne, Laboratoire d'Analyse, Topologie et Probabilités,FST Saint-Jérôme, Case Cour A, Avenue escadrille Normandie-Niemen,13397 Marseille Cedex 20, France

Florence Hubert and Stella Krell

Université de Provence, Laboratoire d'Analyse, Topologie et Probabilités, 39 rue F. Joliot-Curie, 13453 Marseille Cedex 13, France

{dagger} Corresponding author. Email: fboyer{at}cmi.univ-mrs.fr

Received on 22 July 2008. Revised on 21 November 2008.


  Abstract

We propose a nonoverlapping Schwarz algorithm for solving ‘discrete duality finite-volume’ (DDFV) schemes on general meshes. In order to handle this problem the first step is to propose and study a convenient DDFV scheme for anisotropic elliptic problems with mixed Dirichlet/Fourier boundary conditions. Then we are able to build the corresponding Schwarz algorithm and to prove its convergence to the solution of the DDFV scheme on the initial domain. We finally give some numerical results in the case where the Schwarz iterations are used both as a solver and as a preconditioner.

Key Words: finite-volume methods; Schwarz algorithm; DDFV methods


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