IsoGeometric Analysis: Stable elements for the 2D Stokes equation

• Published in: International journal for numerical methods in fluids Vol. 65; no. 11-12; pp. 1407 - 1422
• Main Authors: Buffa, A., de Falco, C., Sangalli, G.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 30-04-2011; Wiley
• Subjects: 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; Isogeometric analysis; B spline; Computational fluid dynamics; Digital simulation; NURBS; Finite element method; incompressibility; Modelling; Incompressible fluid; Viscous fluids; Numerical convergence; stability; Stokes flow
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.2337

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.