Abstract Finite elements of higher continuity, say conforming in H 2 {H^{2}} instead of H 1 {H^{1}} , require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to obtain such mappings given a topologically regular mesh in the standard format of vertex coordinates and a description of the boundary. A variant of the algorithm with orthogonal edges in each vertex is proposed. We introduce necessary modifications in the case of adaptive mesh refinement with nonconforming edges. Furthermore, we discuss efficient storage of the necessary data.

中文翻译：

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四边形和六面体网格上基于有限元的网格单元的可微映射

摘要 具有更高连续性的有限元，例如符合 H 2 {H^{2}} 而不是 H 1 {H^{1}} ，需要从参考单元到网格单元的映射，该映射在单元界面上是连续可微的。在本文中，我们提出了一种算法，在给定顶点坐标标准格式和边界描述的拓扑规则网格的情况下，获得此类映射。提出了在每个顶点中具有正交边的算法的变体。我们在具有不一致边缘的自适应网格细化的情况下引入了必要的修改。此外，我们讨论了必要数据的有效存储。