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arXiv · 1408.2693

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

Michael Feischl·Gregor Gantner·Dirk Praetorius
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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.

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Michael Feischl, Gregor Gantner, Dirk Praetorius. 2014-08-12. Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations. https://doi.org/10.1016/j.cma.2015.03.013

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