A stream virtual element formulation of the Stokes problem on polygonal meshes
Keywords
Advanced Numerical Methods for Scientific Computing
Code:
10/2013
Title:
A stream virtual element formulation of the Stokes problem on polygonal meshes
Date:
Thursday 28th February 2013
Author(s):
Antonietti, P.F.; Beirao da Veiga, L.; Mora, D.; Verani, M.
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Abstract:
In this paper we propose and analyze a novel stream formulation
of the Virtual Element Method (VEM) for the solution of the
Stokes problem. The new formulation hinges upon the introduction
of a suitable stream function space (characterizing the divergence
free subspace of discrete velocities) and it is equivalent to the
velocity-pressure (inf-sup stable) mimetic scheme presented in [L. Beirao da Veiga, V. Gyrya, K. Lipnikov and G. Manzini, Mimetic finite difference method for the Stokes problem on polygonal meshes, J. Comput. Phys. (2009)]
(up to a suitable reformulation into the VEM framework). Both schemes are
thus stable and linearly convergent but the new method results to be more
desirable as it employs much less degrees of freedom and it is based on a
positive definite algebraic problem. Several numerical experiments assess
the convergence properties of the new method and show its computational
advantages with respect to the mimetic one.