Title: Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines,
Abstract: 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. We prove linear
convergence of the error estimator (resp. the sum of energy error plus data
oscillations) with optimal algebraic rates. Numerical experiments underpin the
theoretical findings.