A stream virtual element formulation of the Stokes problem on polygonal meshes
Thursday 28th February 2013
Antonietti, P.F.; Beirao da Veiga, L.; Mora, D.; Verani, M.
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.