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Numerische Mathematik

, Volume 118, Issue 4, pp 737–764 | Cite as

Analysis of a finite volume element method for the Stokes problem

  • Alfio Quarteroni
  • Ricardo Ruiz-BaierEmail author
Article

Abstract

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.

Mathematics Subject Classification (2000)

65N30 35Q30 65N12 65N15 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.CMCS-MATHICSE-SBEcole Polytechnique Fédérale de Lausanne EPFLLausanneSwitzerland
  2. 2.MOX, Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoMilanItaly

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