Analysis of a fi nite volume element method for the Stokes problem
Keywords
Advanced Numerical Methods for Scientific Computing
Code:
10/2010
Title:
Analysis of a fi nite volume element method for the Stokes problem
Date:
Monday 22nd March 2010
Author(s):
Quarteroni, Alfio; Ruiz Baier, Ricardo
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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
di fferent 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. The stabilization of the continuous lowest equal order pair fi nite volume element discretization (P1 - P1) is achieved by enriching the velocity space with bubble-like functions. Finally, some numerical experiments that con firm the predicted behavior of the method are provided.