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Analysis of a finite volume element method for the Stokes problem

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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.

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Authors and Affiliations

  1. CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne EPFL, Station 8, 1015, Lausanne, Switzerland

    Alfio Quarteroni & Ricardo Ruiz-Baier

  2. MOX, Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, via Bonardi 9, 20133, Milan, Italy

    Alfio Quarteroni

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  1. Alfio Quarteroni
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  2. Ricardo Ruiz-Baier
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Correspondence to Ricardo Ruiz-Baier.

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Quarteroni, A., Ruiz-Baier, R. Analysis of a finite volume element method for the Stokes problem. Numer. Math. 118, 737–764 (2011). https://doi.org/10.1007/s00211-011-0373-4

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  • DOI: https://doi.org/10.1007/s00211-011-0373-4

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