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. Beirão da Veiga et al., J. Comput. Phys., 228(2009), pp. 7215-7232] (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.

A stream virtual element formulation of the Stokes problem on polygonal meshes / P.F. Antonietti, L. Beirao Da Veiga, D. Mora, M. Verani. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 52:1(2014), pp. 386-404. [10.1137/13091141X]

A stream virtual element formulation of the Stokes problem on polygonal meshes

L. Beirao Da Veiga
Secondo
;
2014

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. Beirão da Veiga et al., J. Comput. Phys., 228(2009), pp. 7215-7232] (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.
Mimetic finite differences; Polygonal meshes; Stokes problem; Stream function formulation; Virtual elements; Numerical Analysis
Settore MAT/08 - Analisi Numerica
2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/246906
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