Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations

Michael Feischl; Gregor Gantner; Dirk Praetorius

doi:10.1016/j.cma.2015.03.013

Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations

Comput Methods Appl Mech Eng. 2015 Jun 15:290:362-386. doi: 10.1016/j.cma.2015.03.013.

Authors

Michael Feischl¹, Gregor Gantner¹, Dirk Praetorius¹

Affiliation

¹ Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria.

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.

Keywords: A posteriori error estimate; Adaptive mesh-refinement; Boundary element method; Isogeometric analysis.