Publications in Scientific Journals:
G. Gantner, D. Haberlik, D. Praetorius:
"Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines";
Mathematical Models & Methods in Applied Sciences,
27
(2017),
14;
2631
- 2674.
English 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.
Keywords:
Isogeometric analysis; hierarchical splines; adaptivity.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1142/S0218202517500543
Created from the Publication Database of the Vienna University of Technology.