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M. Feischl, G. Gantner, D. Praetorius:
"Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations";
Computer Methods in Applied Mechanics and Engineering, 290 (2015), 362 - 386.

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.

isogeometric analysis, boundary element method, a posteriori error estimate, adaptive mesh-refinement.

http://dx.doi.org/10.1016/j.cma.2015.03.013