Isogeometric analysis of incompressible materials

Isogeometric analysis of incompressible materials

I discuss the application of Isogeometric Analysis to incompressible viscous flow / incompressible elastic material problems. We consider, as a prototype problem, the Stokes system and we propose various choices of inf-sup stable spline spaces for the approximations to the velocity and pressure fields. The proposed choices can be viewed as extensions of the Taylor-Hood, two-level and Raviart-Thomas pairs of finite element spaces. Splines allow for smoother spaces and this improves stability and accuracy of the numerical scheme. We study theoretically and numerically the convergence properties of each method and discuss the conservation properties in each case.