In a recent work (Feischl et al. in Eng Anal Bound Elem 62:141–153, 2016), 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.

中文翻译：

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弱奇异积分方程自适应IGA边界元方法的最优收敛

在最近的一项工作中（Feischl 等人在 Eng Anal Bound Elem 62:141–153, 2016）中，我们分析了二维等几何边界元方法的加权残差估计器，并提出了一种自适应算法，该算法可以引导局部网格细化基础分区的数量以及结的多样性。在目前的工作中，我们给出了一个数学证明，该算法即使在最佳代数率下也能导致收敛。技术贡献包括一种新颖的网格大小函数，该函数还监视节点多重性以及分数阶 Sobolev 范数中 NURBS 的逆估计。