Isogeometric Analysis using a divergence preserving discretization

MSc Jarle Sogn

Nov. 4, 2014, 3:30 p.m. S2 059

We look at the Stokes problem and introduce a divergence preserving isogeometric discretization for this equation. The stability and error estimates of these B-spline spaces have been studied by Evans and Hughes.

Two challenges with these B-spline spaces are that the tangential Dirichlet boundary conditions cannot be strongly imposed and that the transformation required is a divergence preserving transformation and not a component preserving transformation. To weakly impose the Dirichlet boundary conditions we use the Nitsche method and we present numerical results which motivates the need for a sharp Nitsche penalty parameter. Finally we discuss possible preconditioners for our discretization.