Isogeometric Analysis for Incompressible Viscous Flows
The concept of Isogeometric Analysis (IGA) was introduced in [1] with the aim of bridging the gap between computer aided design (CAD) and the finite element method. This aim is pursued by adopting the same Non Uniform Rational B-Spline (NURBS) basis functions to construct both trial and test spaces in the discrete variational formulation of di fferential problems as are used to design domain geometries in CAD applications. As an additional benefi t with respect to standard finite elements, the use of NURBS functions allows to construct fi nite dimensional spaces of higher regularity. In this talk we present the recent results of [2] regarding the application of IGA 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 pressure fields. The proposed choices can be viewed as extensions of the Taylor-Hood, Nédélec and Raviart-Thomas pairs of nite element spaces, respectively. We study the stability and convergence properties of each method and discuss the conservation properties of the discrete velocity eld in each case.