title: 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.
authors.affiliation: Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria.
authors.forename: Michael
authors.initials: M
authors.lastname: Feischl
authors.affiliation: Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria.
authors.forename: Gregor
authors.initials: G
authors.lastname: Gantner
authors.affiliation: Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria.
authors.forename: Dirk
authors.initials: D
authors.lastname: Praetorius
keywords: A posteriori error estimate; Adaptive mesh-refinement; Boundary element method; Isogeometric analysis