  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.
