We derive and discuss a posteriori error estimators for Galerkin and
collocation IGA boundary element methods for weakly-singular integral equations
of the first-kind in 2D. While recent own work considered the Faermann residual
error estimator for Galerkin IGA boundary element methods, the present work
focuses more on collocation and weighted- residual error estimators, which
provide reliable upper bounds for the energy error. Our analysis allows
piecewise smooth parametrizations of the boundary, local mesh-refinement, and
related standard piecewise polynomials as well as NURBS. We formulate an
adaptive algorithm which steers the local mesh-refinement and the multiplicity
of the knots. Numerical experiments show that the proposed adaptive strategy
leads to optimal convergence, and related IGA boundary element methods are
superior to standard boundary element methods with piecewise polynomials.Comment: arXiv admin note: text overlap with arXiv:1408.269
