In this paper we propose a local projector for truncated hierarchical B-splines (THB-splines). The local THB-spline projector is an adaptation of the B\'ezier projector proposed by Thomas et al. (Comput Methods Appl Mech Eng 284, 2015) for B-splines and analysis-suitable T-splines (AS T-splines). For THB-splines, there are elements on which the restrictions of THB-splines are linearly dependent, contrary to B-splines and AS T-splines. Therefore, we cluster certain local mesh elements together such that the THB-splines with support over these clusters are linearly independent, and the B\'ezier projector is adapted to use these clusters. We introduce general extensions for which optimal convergence is shown theoretically and numerically. In addition, a simple adaptive refinement scheme is introduced and compared to Giust et al. (Comput. Aided Geom. Des. 80, 2020), where we find that our simple approach shows promise.

翻译：摘要：本文提出了一种面向截断层次B样条（THB样条）的局部投影算子。该局部THB样条投影算子是对Thomas等人（Comput Methods Appl Mech Eng 284, 2015）针对B样条和适于分析的T样条（AS T样条）提出的Bézier投影算子的改进。与B样条和AS T样条不同，THB样条在某些网格单元上的限制线性相关。因此，我们将部分局部网格单元聚类，使得这些聚类上支撑的THB样条线性无关，并基于此聚类对Bézier投影算子进行适应性改进。本文引入了通用的扩展框架，并从理论与数值两方面证明了其最优收敛性。此外，我们提出了一种简单的自适应细化方案，并与Giust等人（Comput. Aided Geom. Des. 80, 2020）的方案进行了比较，结果表明本文的简单方法具有应用前景。