publisher = {Zenodo},
doi = {10.5281/zenodo.8411345}
}
+
+@misc{Kinnewig2024,
+ title = {Algorithmic realization of the solution to the sign conflict problem for hanging nodes on hp-hexahedral N\'ed\'elec elements},
+ author = {Sebastian Kinnewig and Thomas Wick and Sven Beuchler},
+ year = {2024},
+ eprint = {2306.01416},
+ archivePrefix = {arXiv},
+ primaryClass = {math.NA},
+ url = {https://arxiv.org/abs/2306.01416}
+}
better strategies for refinement of tetrahedra that result in
better-shaped child cells. It also contains
support for cubic finite elements on simplices.
- \item The \texttt{FE\_NedelecSZ} class that contains our
- implementation of the N\'ed\'elec element using the orientation
- scheme of \cite{Zag06} now supports the computation of hanging
- node constraints for locally refined meshes.
- \todo[inline]{Sebastian: Is there anything more to say here, maybe some reference? If
- you want, we can also list this point in the list above, and add
- a whole section 2.x for it. If you think there is nothing more
- that needs to be said, just delete this note.}
+ \item The \texttt{FE\_NedelecSZ} class that contains our
+ implementation of the N\'ed\'elec element using the orientation
+ scheme of \cite{Zag06} now supports the computation of hanging
+ node constraints for locally refined meshes.
+ Therefore, the sign-conflict that arises for hp quadrilateral and
+ hexahedral N\'ed\'elec elements in the presence of hanging edges
+ and hanging faces was addressed for the implementation details;
+ we refer to \cite{Kinnewig2024}.
+ The \texttt{FE\_NedelecSZ} class and the hanging node constraints
+ automatically account for the presence of hanging edges and hanging
+ faces; therefore, there is no difference for the user when using
+ \texttt{FE\_NedelecSZ} as finite elements compared to other finite
+ element classes when used on triangulations with hanging nodes.
+ Note that the special case where, in 3D, more than four cells with
+ different refinement levels share a common edge is not covered yet.
\item The \texttt{AffineConstraints} class stores and processes
constraints on degrees of freedom in \dealii{}. Such constraints
can be of the (homogeneous) form $x_3 = \frac 12 x_{14} + \frac 12 x_{15}$ as is