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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. [ABSTRACT FROM AUTHOR]