Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
Numerical Analysis
2017-06-13 v1
Abstract
In a recent work, we analyzed a weighted-residual error estimator for isogeometric boundary element methods in 2D and proposed an adaptive algorithm which steers the local mesh-refinement of the underlying partition as well as the multiplicity of the knots. In the present work, we give a mathematical proof that this algorithm leads to convergence even with optimal algebraic rates. Technical contributions include a novel mesh-size function which also monitors the knot multiplicity as well as inverse estimates for NURBS in fractional-order Sobolev norms.
Cite
@article{arxiv.1510.05111,
title = {Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations},
author = {Michael Feischl and Gregor Gantner and Alexander Haberl and Dirk Praetorius},
journal= {arXiv preprint arXiv:1510.05111},
year = {2017}
}