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Journal of Scientific Computing

, Volume 65, Issue 3, pp 956–978 | Cite as

Equal Order Discontinuous Finite Volume Element Methods for the Stokes Problem

  • Sarvesh Kumar
  • Ricardo Ruiz-Baier
Article

Abstract

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 \(L^2\)-norm under the assumption that the source term is locally in \( H^1\). Several numerical experiments in two and three spatial dimensions are presented to validate our theoretical findings.

Keywords

Stokes equations Discontinuous Galerkin methods Stabilization Finite volume element methods Error analysis 

Mathematics Subject Classification

65N08 65N12 76D07 65N15 

Notes

Acknowledgments

We thank Dr. Thirupathi Gudi (IISc, Bangalore) for his valuable suggestions during the early stage of this work, and we gratefully acknowledge the support by the University of Lausanne.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Space Science and TechnologyThiruvananthapuramIndia
  2. 2.Institut des Sciences de la Terre, FGSEUniversité de Lausanne, Géopolis Quartier Unil-MoulineLausanneSwitzerland

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