In this article, the construction of versatile transition elements for applications in dynamics is comprehensively discussed. Based on the transfinite mapping technique, also known as Coons–Gordon interpolation, piece-wise shape functions are derived such that an arbitrary number of elements with different ansatz spaces is coupled conformingly. This is an important prerequisite to enable the use of local mesh refinement strategies for regular quadrilateral discretizations. Due to the special construction of the shape functions, there are no hanging nodes that need to be taken care of. The focus in this contribution is on dynamics, and therefore, Lagrange polynomials are taken as the basis to construct shape functions for arbitrary transition elements. As a consequence, the Kronecker-delta and partition of unity properties are recovered. These properties are crucial to diagonalize the mass matrix using standard mass lumping techniques such as row-summing and diagonal scaling. The performance of the proposed family of elements is assessed by means of several benchmark examples, where the numerical rates of convergence are determined for both consistent and lumped mass matrix formulations.

在本文中，全面讨论了用于动力学应用的通用过渡元素的构建。基于超限映射技术，也称为 Coons-Gordon 插值，可以导出分段形状函数，从而使具有不同 ansatz 空间的任意数量的元素一致耦合。这是使局部网格细化策略能够用于常规四边形离散化的重要先决条件。由于形状函数的特殊构造，没有需要照顾的悬挂节点。此贡献的重点是动力学，因此，拉格朗日多项式作为构造任意过渡元素形状函数的基础。结果，恢复了统一属性的 Kronecker-delta 和分区。这些属性对于使用标准质量集总技术（例如行求和和对角线缩放）对角化质量矩阵至关重要。提议的元素族的性能通过几个基准示例进行评估，其中确定了一致和集总质量矩阵公式的数值收敛率。