While working with Nédélec 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 Nédélec 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. 

The work is done by Sebastian Kinnewig, Thomas Wick, Sven Beuchler within the team led by  Prof. Thomas Wick

The original publication is available at https://arxiv.org/abs/2306.01416

Read more and download the code from here:  
https://github.com/tommeswick
https://github.com/kinnewig