Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations
Abstract
We consider the Galerkin boundary element method (BEM) for weakly-singular integral equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the unknown Galerkin BEM error. The required assumptions are weak and allow for piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. In particular, our analysis gives a first contribution to adaptive BEM in the frame of isogeometric analysis (IGABEM), for which we formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments underline the theoretical findings and show that the proposed adaptive strategy leads to optimal convergence.
Cite
@article{arxiv.1408.2693,
title = {Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations},
author = {Michael Feischl and Gregor Gantner and Dirk Praetorius},
journal= {arXiv preprint arXiv:1408.2693},
year = {2015}
}