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G. Gantner, D. Haberlik, D. Praetorius:
"Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines";
in: "ASC Report 02/2017", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2017, ISBN: 978-3-902627-10-0, 1 - 37.

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.

Isogeometric analysis; hierarchical splines; adaptivity.

http://www.asc.tuwien.ac.at/preprint/2017/asc02x2017.pdf