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arXiv · 1510.05111

Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations

Michael Feischl·Gregor Gantner·Alexander Haberl·Dirk Praetorius
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Abstract

In a recent work, we analyzed a weighted-residual error estimator for isogeometric boundary element methods in 2D and proposed an adaptive algorithm which steers the local mesh-refinement of the underlying partition as well as the multiplicity of the knots. In the present work, we give a mathematical proof that this algorithm leads to convergence even with optimal algebraic rates. Technical contributions include a novel mesh-size function which also monitors the knot multiplicity as well as inverse estimates for NURBS in fractional-order Sobolev norms.

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Michael Feischl, Gregor Gantner, Alexander Haberl, Dirk Praetorius. 2015-10-17. Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. https://doi.org/10.1007/s00211-016-0836-8

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