While working with N\'ed\'elec elements on adaptively refined meshes with hanging nodes, the orientation of the hanging edges and faces must be taken into account. Indeed, for non-orientable meshes, there was no solution and implementation available to date. The problem statement and corresponding algorithms are described in great detail. As a model problem, the time-harmonic Maxwell's equations are adopted because N\'ed\'elec elements constitute their natural discretization. The implementation is performed within the finite element library deal.II. The algorithms and implementation are demonstrated through four numerical examples on different uniformly and adaptively refined meshes.

翻译：在使用Nédélec单元处理含悬挂节点的自适应加密网格时，必须考虑悬挂边和悬挂面的取向问题。事实上，对于不可定向网格，目前尚无现成的解决方案和实现方法。本文详细描述了问题陈述及其对应算法。以时谐麦克斯韦方程组作为模型问题，因为Nédélec单元是其天然离散化工具。该实现基于有限元库deal.II完成。通过四个不同均匀和自适应加密网格上的数值算例，展示了相关算法与实现过程。