Adaptive isogeometric methods with hierarchical splines: Optimality and convergence rates

We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and continue the study of its numerical properties. We prove that our AIGM is optimal in the sense that delivers optimal convergence rates as soon as the solution of the underlying partial differential equation belongs to a suitable approximation class. The main tool we use is the theory of adaptive methods, together with a local upper bound for the residual error indicators based on suitable properties of a well selected quasi-interpolation operator on hierarchical spline spaces.

Published in:
Mathematical Models and Methods in Applied Sciences, 27, 14, 2781-2802
Jun 01 2018
Other identifiers:

Note: The status of this file is: Anyone

 Record created 2018-05-16, last modified 2019-12-05

Download fulltextPDF Download fulltextPDF (PDFA)
Rate this document:

Rate this document:
(Not yet reviewed)