This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method (FEM) and the boundary element method (BEM) in the frame of isogeometric analysis (IGA).

翻译：本文件回顾了最新技术,并讨论了适应性等分数分析领域的最新动态,特别侧重于数学理论,其中包括概述可用于当地解决可能奇点的现有样板技术,以及在等分数分析框架内有限元素法和边界元素法的适应性算法趋同和准优化的最新设计。