Fulltext

Equal Order Discontinuous Finite Volume Element Methods for the Stokes Problem

Kumar, Sarvesh ; Ruiz-Baier, Ricardo

In: Journal of Scientific Computing, 2015, vol. 65, no. 3, p. 956-978

Ajouter à la liste personnelle
    Titre
    • Equal Order Discontinuous Finite Volume Element Methods for the Stokes Problem
    Auteur
    • Kumar, Sarvesh. Department of Mathematics, Indian Institute of Space Science and Technology, 695 547, Thiruvananthapuram, Kerala, India
    • Ruiz-Baier, Ricardo. Institut des Sciences de la Terre, FGSE, Université de Lausanne, Géopolis Quartier Unil-Mouline, 1015, Lausanne, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Scientific Computing, 2015, vol. 65, no. 3, p. 956-978. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:331109
    Summary
    The aim of this paper is to develop and analyze a family of stabilized discontinuous finite volume element methods for the Stokes equations in two and three spatial dimensions. The proposed scheme is constructed using a baseline finite element approximation of velocity and pressure by discontinuous piecewise linear elements, where an interior penalty stabilization is applied. A priori error estimates are derived for the velocity and pressure in the energy norm, and convergence rates are predicted for velocity in the $$L^2$$ L 2 -norm under the assumption that the source term is locally in $$ H^1$$ H 1 . Several numerical experiments in two and three spatial dimensions are presented to validate our theoretical findings.