One of the most appealing techniques in local refinement for isogeometric analysis (IGA) is hierarchical B‐splines which can be improved by resorting to truncation mechanism called truncated hierarchical B‐splines. Although it has a simple concept, it involves implementing the hierarchical definition of shape functions to existing codes. In this contribution, we present a simple method defined by knot vectors of different levels of hierarchical meshes resulted from knot insertion techniques. In fact, the proposed method is a generalization of the classical Bézier extraction with an element viewpoint which enhances the procedure of adaptive finite element analysis in error estimation based on marking of the elements. This results in an adaptive IGA based on multilevel extraction to the hierarchical overlay of functions. The convergence and computational efficiency of the proposed method are demonstrated through benchmark examples.

中文翻译：

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自适应等几何分析中多级局部细化的新见解

局部细化等几何分析（IGA）中最吸引人的技术之一是分层B样条曲线，可以通过采用称为截短分层B样条线的截断机制来进行改进。尽管它有一个简单的概念，但它涉及对现有代码实施形状函数的分层定义。在这一贡献中，我们提出了一种简单的方法，该方法由结插入技术产生的不同级别的分层网格的结矢量定义。实际上，所提出的方法是基于元素观点的经典Bézier提取的概括，它增强了基于元素标记的误差估计中自适应有限元分析的过程。这导致基于对功能的分层覆盖的多级提取的自适应IGA。