Adaptive IGAFEM with optimal convergence rates: T-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. We employ analysis-suitable T-splines of arbitrary odd degree on T-meshes generated by the refinement strategy of [Morgenstern, Peterseim, Comput. Aided Geom. Design 34 (2015)] in 2D and [Morgenstern, SIAM J. Numer. Anal. 54 (2016)] in 3D. Adaptivity is driven by some weighted residual a posteriori error estimator. We prove linear convergence of the error estimator (which is equivalent to the sum of energy error plus data oscillations) with optimal algebraic rates with respect to the number of elements of the underlying mesh.
Cite
@article{arxiv.1910.01311,
title = {Adaptive IGAFEM with optimal convergence rates: T-splines},
author = {Gregor Gantner and Dirk Praetorius},
journal= {arXiv preprint arXiv:1910.01311},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1701.07764