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Analysis of a finite volume element method for the Stokes problem

Quarteroni, Alfio ; Ruiz-Baier, Ricardo

In: Numerische Mathematik, 2011, vol. 118, no. 4, p. 737-764

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    Titre
    • Analysis of a finite volume element method for the Stokes problem
    Auteur
    • Quarteroni, Alfio. CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne EPFL, Station 8, 1015, Lausanne, Switzerland
    • Ruiz-Baier, Ricardo. CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne EPFL, Station 8, 1015, Lausanne, Switzerland
    Type de document
    • Postprint
    Classification
    • Informatique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:310954
    Summary
    In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided