Adaptive IGAFEM with optimal convergence rates: hierarchical B-splines

Gregor Gantner, Daniel Haberlik, Dirk Praetorius

Published 2017-01-26Version 1

We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ hierarchical B-splines of arbitrary degree and different order of smoothness. We propose a refinement strategy to generate a sequence of locally refined meshes and corresponding discrete solutions. Adaptivity is driven by some weighted residual a posteriori error estimator.