IsoGeometric Analysis: Stable elements for the 2D Stokes equation

In this paper, we discuss the application of IsoGeometric Analysis to incompressible viscous flow problems. We consider, as a prototype problem, the Stokes system and we propose various choices of compatible spline spaces for the approximations to the velocity and the pressure fields. The proposed c...

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Veröffentlicht in:	International journal for numerical methods in fluids 2011-04, Vol.65 (11-12), p.1407-1422
Hauptverfasser:	Buffa, A., de Falco, C., Sangalli, G.
Format:	Artikel
Sprache:	eng
Schlagworte:	Computational methods in fluid dynamics Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) incompressibility IsoGeometric Analysis Laminar flows Low-reynolds-number (creeping) flows NURBS Physics stability Stokes flow
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Beschreibung
Zusammenfassung:	In this paper, we discuss the application of IsoGeometric Analysis to incompressible viscous flow problems. We consider, as a prototype problem, the Stokes system and we propose various choices of compatible spline spaces for the approximations to the velocity and the pressure fields. The proposed choices can be viewed as extensions of the Taylor–Hood, Nédélec and Raviart–Thomas pairs of finite element spaces, respectively. We study the stability and convergence properties of each method and discuss the conservation properties of the discrete velocity field in each case. Copyright © 2010 John Wiley & Sons, Ltd.
ISSN:	0271-2091 1097-0363
DOI:	10.1002/fld.2337