Feischl Michael, Gantner Gregor, Haberl Alexander, Praetorius Dirk
The Red Centre, School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052 Australia.
Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria.
Numer Math (Heidelb). 2017;136(1):147-182. doi: 10.1007/s00211-016-0836-8. Epub 2016 Aug 11.
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.
在最近的一项工作中（费施尔等人，《工程分析中的边界元》，第62卷，第141 - 153页，2016年），我们分析了二维等几何边界元方法的加权残差误差估计器，并提出了一种自适应算法，该算法可指导基础剖分的局部网格细化以及节点的重数。在当前工作中，我们给出了一个数学证明，即该算法即使以最优代数速率也能收敛。技术贡献包括一个新颖的网格尺寸函数，它还能监测节点重数以及分数阶索伯列夫范数下NURBS的逆估计。
